See also the Gretl Command Reference
The following accessors and functions are documented below.Must follow the estimation of a fixed-effect panel data model. Returns a series containing the estimates of the individual fixed effects (per-unit intercepts).
Returns the Akaike Information Criterion for the last estimated model, if available. See chapter 23 of the Gretl User's Guide for details of the calculation.
Returns Schwarz's Bayesian Information Criterion for the last estimated model, if available. See chapter 23 of the Gretl User's Guide for details of the calculation.
Returns the overall chi-square statistic from the last estimated model, if available.
Argument: | s (name of coefficient, optional) |
With no arguments, $coeff returns a column vector containing the estimated coefficients for the last model. With the optional string argument it returns a scalar, namely the estimated parameter named s. See also $stderr, $vcv.
Example:
open bjg arima 0 1 1 ; 0 1 1 ; lg b = $coeff # gets a vector macoef = $coeff(theta_1) # gets a scalar
If the "model" in question is actually a system, the result depends on the characteristics of the system: for VARs and VECMs the value returned is a matrix with one column per equation, otherwise it is a column vector containing the coefficients from the first equation followed by those from the second equation, and so on.
Must follow the estimation of a model; returns the command word, for example ols or probit.
Must follow the estimation of a VAR or a VECM; returns the companion matrix.
Returns an integer value representing the sort of dataset that is currently loaded: 0 = no data; 1 = cross-sectional (undated) data; 2 = time-series data; 3 = panel data.
Must follow the estimation of a single-equation model; returns the name of the dependent variable.
Returns the degrees of freedom of the last estimated model. If the last model was in fact a system of equations, the value returned is the degrees of freedom per equation; if this differs across the equations then the value given is the number of observations minus the mean number of coefficients per equation (rounded up to the nearest integer).
Must follow estimation of a system of equations. Returns the P-value associated with the $diagtest statistic.
Must follow estimation of a system of equations. Returns the test statistic for the null hypothesis that the cross-equation covariance matrix is diagonal. This is the Breusch–Pagan test except when the estimator is (unrestricted) iterated SUR, in which case it is a Likelihood Ratio test. See chapter 28 of the Gretl User's Guide for details; see also $diagpval.
Returns the p-value for the Durbin–Watson statistic for the model last estimated (if available), computed using the Imhof procedure.
Due to the limited precision of computer arithmetic, the Imhof integral can go negative when the Durbin–Watson statistic is close to its lower bound. In that case the accessor returns NA. Since any other failure mode results in an error being flagged it is probably safe to assume that an NA value means the true p-value is "very small", although we are unable to quantify it.
Must follow the estimation of a VECM; returns a matrix containing the error correction terms. The number of rows equals the number of observations used and the number of columns equals the cointegration rank of the system.
Returns the program's internal error code, which will be non-zero in case an error has occurred but has been trapped using catch. Note that using this accessor causes the internal error code to be reset to zero. If you want to get the error message associated with a given $error you need to store the value in a temporary variable, as in
err = $error if (err) printf "Got error %d (%s)\n", err, errmsg(err); endif
Returns the error sum of squares of the last estimated model, if available.
Must follow the estimation of a VECM; returns a vector containing the eigenvalues that are used in computing the trace test for cointegration.
Must follow the fcast forecasting command; returns the forecast values as a matrix. If the model on which the forecast was based is a system of equations the returned matrix will have one column per equation, otherwise it is a column vector.
Must follow the fcast forecasting command; returns the standard errors of the forecasts, if available, as a matrix. If the model on which the forecast was based is a system of equations the returned matrix will have one column per equation, otherwise it is a column vector.
Must follow estimation of a VAR. Returns a matrix containing the forecast error variance decomposition (FEVD). This matrix has h rows where h is the forecast horizon, which can be chosen using set horizon or otherwise is set automatically based on the frequency of the data.
For a VAR with p variables, the matrix has p^{2} columns: the first p columns contain the FEVD for the first variable in the VAR; the second p columns the FEVD for the second variable; and so on. The (decimal) fraction of the forecast error for variable i attributable to innovation in variable j is therefore found in column (i – 1)p + j.
Returns the overall F-statistic from the last estimated model, if available.
Must follow a gmm block. Returns the value of the GMM objective function at its minimum.
Must follow a garch command. Returns the estimated conditional variance series.
Must follow estimation of a model via either tsls or panel with the random effects option. Returns a 1 x 3 vector containing the value of the Hausman test statistic, the corresponding degrees of freedom and the p-value for the test, in that order.
Returns the Hannan-Quinn Information Criterion for the last estimated model, if available. See chapter 23 of the Gretl User's Guide for details of the calculation.
Returns a very large positive number. By default this is 1.0E100, but the value can be changed using the set command.
Must follow the estimation of a VECM, and returns the loadings matrix. It has as many rows as variables in the VECM and as many columns as the cointegration rank.
Must follow the estimation of a VECM, and returns the cointegration matrix. It has as many rows as variables in the VECM (plus the number of exogenous variables that are restricted to the cointegration space, if any), and as many columns as the cointegration rank.
Must follow the estimation of a VECM, and returns the estimated covariance matrix for the elements of the cointegration vectors.
In the case of unrestricted estimation, this matrix has a number of rows equal to the unrestricted elements of the cointegration space after the Phillips normalization. If, however, a restricted system is estimated via the restrict command with the --full option, a singular matrix with (n+m)r rows will be returned (n being the number of endogenous variables, m the number of exogenous variables that are restricted to the cointegration space, and r the cointegration rank).
Example: the code
open denmark.gdt vecm 2 1 LRM LRY IBO IDE --rc --seasonals -q s0 = $jvbeta restrict --full b[1,1] = 1 b[1,2] = -1 b[1,3] + b[1,4] = 0 end restrict s1 = $jvbeta print s0 print s1
produces the following output.
s0 (4 x 4) 0.019751 0.029816 -0.00044837 -0.12227 0.029816 0.31005 -0.45823 -0.18526 -0.00044837 -0.45823 1.2169 -0.035437 -0.12227 -0.18526 -0.035437 0.76062 s1 (5 x 5) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.27398 -0.27398 -0.019059 0.0000 0.0000 -0.27398 0.27398 0.019059 0.0000 0.0000 -0.019059 0.019059 0.0014180
Returns a string representing the national language in force currently, if this can be determined. The string is composed of a two-letter ISO 639-1 language code (for example, en for English, jp for Japanese, el for Greek) followed by an underscore plus a two-letter ISO 3166-1 country code. Thus for example Portuguese in Portugal gives pt_PT while Portuguese in Brazil gives pt_BR.
If the national language cannot be determined, the string "unknown" is returned.
For selected models estimated via Maximum Likelihood, returns the series of per-observation log-likelihood values. At present this is supported only for binary logit and probit, tobit and heckit.
Returns the log-likelihood for the last estimated model (where applicable).
Returns the value of "machine epsilon", which gives an upper bound on the relative error due to rounding in double-precision floating point arithmetic.
Following estimation of a multinomial logit model (only), retrieves a matrix holding the estimated probabilities of each possible outcome at each observation in the model's sample range. Each row represents an observation and each column an outcome.
Returns the total number of coefficients estimated in the last model.
Returns the number of observations in the currently selected sample.
Returns the number of variables in the dataset (including the constant).
Applicable when the current dataset is time-series with annual, quarterly, monthly or decennial frequency, or is dated daily or weekly, or when the dataset is a panel with time-series information set appropriately (see the setobs command). The returned series holds 8-digit numbers on the pattern YYYYMMDD (ISO 8601 "basic" date format), which correspond to the day of the observation, or the first day of the observation period in case of a time-series frequency less than daily.
Such a series can be helpful when using the join command.
Applicable when the observations in the current dataset have a major:minor structure, as in quarterly time series (year:quarter), monthly time series (year:month), hourly data (day:hour) and panel data (individual:period). Returns a series holding the major or low-frequency component of each observation (for example, the year).
See also $obsminor, $obsmicro.
Applicable when the observations in the current dataset have a major:minor:micro structure, as in dated daily time series (year:month:day). Returns a series holding the micro or highest-frequency component of each observation (for example, the day).
See also $obsmajor, $obsminor.
Applicable when the observations in the current dataset have a major:minor structure, as in quarterly time series (year:quarter), monthly time series (year:month), hourly data (day:hour) and panel data (individual:period). Returns a series holding the minor or high-frequency component of each observation (for example, the month).
In the case of dated daily data, $obsminor gets the month of each observation.
See also $obsmajor, $obsmicro.
Returns the frequency or periodicity of the data (e.g. 4 for quarterly data). In the case of panel data the value returned is the time-series length.
Returns the value of π in double precision.
Returns the p-value of the test statistic that was generated by the last explicit hypothesis-testing command, if any (for example, chow). See chapter 9 of the Gretl User's Guide for details.
In most cases the return value is a scalar but sometimes it is a matrix (for example, the trace and lambda-max p-values from the Johansen cointegration test); in that case the values in the matrix are laid out in the same pattern as the printed results.
See also $test.
Must follow an invocation of the qlrtest command (the QLR test for a structural break at an unknown point). The value returned is the 1-based index of the observation at which the test statistic is maximized.
Argument: | n (scalar, optional) |
Without arguments, returns the first-order autoregressive coefficient for the residuals of the last model. After estimating a model via the ar command, the syntax $rho(n) returns the corresponding estimate of ρ(n).
Returns the unadjusted R^{2} from the last estimated model, if available.
Must follow estimation of a single-equation model. Returns a dummy series with value 1 for observations used in estimation, 0 for observations within the currently defined sample range but not used (presumably because of missing values), and NA for observations outside of the current range.
If you wish to compute statistics based on the sample that was used for a given model, you can do, for example:
ols y 0 xlist genr sdum = $sample smpl sdum --dummy
Must follow a tsls command. Returns a 1 x 3 vector, containing the value of the Sargan over-identification test statistic, the corresponding degrees of freedom and p-value, in that order. If the model is exactly identified, the statistic is unavailable, and trying to access it provokes an error.
Requires that a model has been estimated. If the last model was a single equation, returns the (scalar) Standard Error of the Regression (or in other words, the standard deviation of the residuals, with an appropriate degrees of freedom correction). If the last model was a system of equations, returns the cross-equation covariance matrix of the residuals.
Argument: | s (name of coefficient, optional) |
With no arguments, $stderr returns a column vector containing the standard error of the coefficients for the last model. With the optional string argument it returns a scalar, namely the standard error of the parameter named s.
If the "model" in question is actually a system, the result depends on the characteristics of the system: for VARs and VECMs the value returned is a matrix with one column per equation, otherwise it is a column vector containing the coefficients from the first equation followed by those from the second equation, and so on.
Must be preceded by set stopwatch, which activates the measurement of CPU time. The first use of this accessor yields the seconds of CPU time that have elapsed since the set stopwatch command. At each access the clock is reset, so subsequent uses of $stopwatch yield the seconds of CPU time since the previous access.
Must follow estimation of a simultaneous equations system. Returns the matrix of coefficients on the lagged endogenous variables, if any, in the structural form of the system. See the system command.
Must follow estimation of a simultaneous equations system. Returns the matrix of coefficients on the exogenous variables in the structural form of the system. See the system command.
Must follow estimation of a simultaneous equations system. Returns the matrix of coefficients on the contemporaneous endogenous variables in the structural form of the system. See the system command.
Returns a bundle containing information on the capabilities of the gretl build and the system on which gretl is running. The members of the bundle are as follows:
mpi: integer, equals 1 if the system supports MPI (Message Passing Interface), otherwise 0.
omp: integer, equals 1 if gretl is built with support for Open MP, otherwise 0.
nproc: integer, the number of processors available.
mpimax: integer, the maximum number of MPI processes that can be run in parallel. This is zero if MPI is not supported, otherwise it equals the local nproc value unless an MPI hosts file has been specified, in which case it is the sum of the number of processors or "slots" across all the machines referenced in that file.
wordlen: integer, either 32 or 64 for 32- and 64-bit systems respectively.
os: string representing the operating system, either linux, osx, windows or other.
hostname: the name of the host machine on which the current gretl process is running (with a fallback of localhost in case the name cannot be determined).
Note that individual elements in the bundle can be accessed using "dot" notation without any need to copy the whole bundle under a user-specified name. For example,
if $sysinfo.os == "linux" # do something linux-specific endif
Returns the number of observations used in estimating the last model.
Returns the 1-based index of the first observation in the currently selected sample.
Returns the 1-based index of the last observation in the currently selected sample.
Returns the value of the test statistic that was generated by the last explicit hypothesis-testing command, if any (e.g. chow). See chapter 9 of the Gretl User's Guide for details.
In most cases the return value is a scalar but sometimes it is a matrix (for example, the trace and lambda-max statistics from the Johansen cointegration test); in that case the values in the matrix are laid out in the same pattern as the printed results.
See also $pvalue.
Returns TR^{2} (sample size times R-squared) from the last model, if available.
Returns the residuals from the last model. This may have different meanings for different estimators. For example, after an ARMA estimation $uhat will contain the one-step-ahead forecast error; after a probit model, it will contain the generalized residuals.
If the "model" in question is actually a system (a VAR or VECM, or system of simultaneous equations), $uhat with no parameters retrieves the matrix of residuals, one column per equation.
Valid for panel datasets only. Returns a series with value 1 for all observations on the first unit or group, 2 for observations on the second unit, and so on.
Arguments: | s1 (name of coefficient, optional) |
s2 (name of coefficient, optional) |
With no arguments, $vcv returns a square matrix containing the estimated covariance matrix for the coefficients of the last model. If the last model was a single equation, then you may supply the names of two parameters in parentheses to retrieve the estimated covariance between the parameters named s1 and s2. See also $coeff, $stderr.
This accessor is not available for VARs or VECMs; for models of that sort see $sigma and $xtxinv.
Must follow the estimation of a VECM; returns a matrix in which the Gamma matrices (coefficients on the lagged differences of the cointegrated variables) are stacked side by side. Each row represents an equation; for a VECM of lag order p there are p – 1 sub-matrices.
Returns an integer value that codes for the program version. The current gretl version string takes the form of a 4-digit year followed by a letter from a to j representing the sequence of releases within the year (for example, 2015d). The return value from this accessor is formed as 10 times the year plus the zero-based lexical order of the letter, so 2015d translates to 20153.
Prior to gretl 2015d, version identifiers took the form x.y.z (three integers separated by dots), and in that case the accessor value was calculated as 10000*x + 100*y + z, so that for example 1.10.2 (the last release under the old scheme) translates as 11002. Numerical order of $version values is therefore preserved across the change in versioning scheme.
Must follow the estimation of a VAR or a VECM; returns a matrix containing the VMA representation up to the order specified via the set horizon command. See chapter 26 of the Gretl User's Guide for details.
Returns 1 if gretl is running on MS Windows, otherwise 0. By conditioning on the value of this variable you can write shell calls that are portable across different operating systems.
Also see the shell command.
If the last model was a single equation, returns the list of regressors. If the last model was a system of equations, returns the "global" list of exogenous and predetermined variables (in the same order in which they appear in $sysB). If the last model was a VAR, returns the list of exogenous regressors, if any.
Following estimation of a VAR or VECM (only), returns X'X^{-1}, where X is the common matrix of regressors used in each of the equations. This accessor is not available for a VECM estimated with a restriction imposed on α, the "loadings" matrix.
Returns the fitted values from the last regression.
If the last model estimated was a VAR, VECM or simultaneous system, returns the associated list of endogenous variables. If the last model was a single equation, this accessor gives a list with a single element, the dependent variable. In the special case of the biprobit model the list contains two elements.
Argument: | x (scalar, series or matrix) |
Returns the absolute value of x.
Argument: | x (scalar, series or matrix) |
Returns the arc cosine of x, that is, the value whose cosine is x. The result is in radians; the input should be in the range –1 to 1.
Argument: | x (scalar, series or matrix) |
Returns the inverse hyperbolic cosine of x (positive solution). x should be greater than 1; otherwise, NA is returned. See also cosh.
Arguments: | x (series or list) |
byvar (series or list) | |
funcname (string) |
In the simplest version, both x and byvar are individual series. In that case this function returns a matrix with three columns: the first holds the distinct values of byvar, sorted in ascending order; the second holds the count of observations at which byvar takes on each of these values; and the third holds the values of the statistic specified by funcname calculated on series x, using only those observations at which byvar takes on the value given in the first column.
More generally, if byvar is a list with n members then the left-hand n columns hold the combinations of the distinct values of each of the n series and the count column holds the number of observations at which each combination is realized. If x is a list with m members then the rightmost m columns hold the values of the specified statistic for each of the x variables, again calculated on the sub-sample indicated in the first column(s).
The following values of funcname are supported "natively": sum, sumall, mean, sd, var, sst, skewness, kurtosis, min, max, median, nobs and gini. Each of these functions takes a series argument and returns a scalar value, and in that sense can be said to "aggregate" the series in some way. You may give the name of a user-defined function as the aggregator; like the built-ins, such a function must take a single series argument and return a scalar value.
Note that although a count of cases is provided automatically the nobs function is not redundant as an aggregator, since it gives the number of valid (non-missing) observations on x at each byvar combination.
For a simple example, suppose that region represents a coding of geographical region using integer values 1 to n, and income represents household income. Then the following would produce an n x 3 matrix holding the region codes, the count of observations in each region, and mean household income for each of the regions:
matrix m = aggregate(income, region, mean)
For an example using lists, let gender be a male/female dummy variable, let race be a categorical variable with three values, and consider the following:
list BY = gender race list X = income age matrix m = aggregate(X, BY, sd)
The aggregate call here will produce a 6 x 5 matrix. The first two columns hold the 6 distinct combinations of gender and race values; the middle column holds the count for each of these combinations; and the rightmost two columns contain the sample standard deviations of income and age.
Note that if byvar is a list, some combinations of the byvar values may not be present in the data (giving a count of zero). In that case the value of the statistics for x are recorded as NaN (not a number). If you want to ignore such cases you can use the selifr function to select only those rows that have a non-zero count. The column to test is one place to the right of the number of byvar variables, so we can do:
matrix m = aggregate(X, BY, sd) scalar c = nelem(BY) m = selifr(m, m[,c+1])
Argument: | s (string) |
For s the name of a parameter to a user-defined function, returns the name of the corresponding argument, or an empty string if the argument was anonymous.
Argument: | n (integer) |
The basic "constructor" function for a new array variable. In using this function you must specify a type (in plural form) for the array: strings, matrices, bundles or lists. The return value is an array of the specified type with n elements, each of which is initialized as "empty" (e.g. zero-length string, null matrix). Examples of usage:
strings S = array(5) matrices M = array(3)
Argument: | x (scalar, series or matrix) |
Returns the arc sine of x, that is, the value whose sine is x. The result is in radians; the input should be in the range –1 to 1.
Argument: | x (scalar, series or matrix) |
Returns the inverse hyperbolic sine of x. See also sinh.
Argument: | x (scalar, series or matrix) |
Returns the arc tangent of x, that is, the value whose tangent is x. The result is in radians.
Argument: | x (scalar, series or matrix) |
Returns the inverse hyperbolic tangent of x. See also tanh.
Argument: | s (string) |
Closely related to the C library function of the same name. Returns the result of converting the string s (or the leading portion thereof, after discarding any initial white space) to a floating-point number. Unlike C's atof, however, the decimal character is always assumed (for reasons of portability) to be ".". Any characters that follow the portion of s that converts to a floating-point number under this assumption are ignored.
If none of s (following any discarded white space) is convertible under the stated assumption, NA is returned.
# examples x = atof("1.234") # gives x = 1.234 x = atof("1,234") # gives x = 1 x = atof("1.2y") # gives x = 1.2 x = atof("y") # gives x = NA x = atof(",234") # gives x = NA
See also sscanf for more flexible string to numeric conversion.
Arguments: | type (character) |
v (scalar) | |
x (scalar, series or matrix) |
Computes one of the Bessel function variants for order v and argument x. The return value is of the same type as x. The specific function is selected by the first argument, which must be J, Y, I, or K. A good discussion of the Bessel functions can be found on Wikipedia; here we give a brief account.
case J: Bessel function of the first kind. Resembles a damped sine wave. Defined for real v and x, but if x is negative then v must be an integer.
case Y: Bessel function of the second kind. Defined for real v and x but has a singularity at x = 0.
case I: Modified Bessel function of the first kind. An exponentially growing function. Acceptable arguments are as for case J.
case K: Modified Bessel function of the second kind. An exponentially decaying function. Diverges at x = 0 and is not defined for negative x. Symmetric around v = 0.
Arguments: | &b (reference to matrix) |
f (function call) | |
g (function call, optional) |
Numerical maximization via the method of Broyden, Fletcher, Goldfarb and Shanno. On input the vector b should hold the initial values of a set of parameters, and the argument f should specify a call to a function that calculates the (scalar) criterion to be maximized, given the current parameter values and any other relevant data. If the object is in fact minimization, this function should return the negative of the criterion. On successful completion, BFGSmax returns the maximized value of the criterion, and b holds the parameter values which produce the maximum.
The optional third argument provides a means of supplying analytical derivatives (otherwise the gradient is computed numerically). The gradient function call g must have as its first argument a pre-defined matrix that is of the correct size to contain the gradient, given in pointer form. It also must take the parameter vector as an argument (in pointer form or otherwise). Other arguments are optional.
For more details and examples see the chapter on numerical methods in chapter 31 of the Gretl User's Guide. See also BFGScmax, NRmax, fdjac, simann.
Arguments: | &b (reference to matrix) |
bounds (matrix) | |
f (function call) | |
g (function call, optional) |
Constrained numerical maximization using L-BFGS-B (limited memory BFGS, see Byrd, Lu, Nocedal and Zhu, 1995). On input the vector b should hold the initial values of a set of parameters, bounds should hold bounds on the parameter values (see below), and f should specify a call to a function that calculates the (scalar) criterion to be maximized, given the current parameter values and any other relevant data. If the object is in fact minimization, this function should return the negative of the criterion. On successful completion, BFGScmax returns the maximized value of the criterion, subject to the constraints in bounds, and b holds the parameter values which produce the maximum.
The bounds matrix must have 3 columns and as many rows are there are constrained elements in the parameter vector. The first element on a given row is the (1-based) index of the constrained parameter; the second and third are the lower and upper bounds, respectively. The values -$huge and $huge should be used to indicate that the parameter is unconstrained downward or upward, respectively. For example, the following is the way to specify that the second element of the parameter vector must be non-negative:
matrix bounds = {2, 0, $huge}
The optional third argument provides a means of supplying analytical derivatives (otherwise the gradient is computed numerically). The gradient function call g must have as its first argument a pre-defined matrix that is of the correct size to contain the gradient, given in pointer form. It also must take the parameter vector as an argument (in pointer form or otherwise). Other arguments are optional.
For more details and examples see the chapter on numerical methods in chapter 31 of the Gretl User's Guide. See also BFGSmax, NRmax, fdjac, simann.
Arguments: | y (series) |
f1 (integer, optional) | |
f2 (integer, optional) | |
k (integer, optional) |
Returns the result from application of the Baxter–King bandpass filter to the series y. The optional parameters f1 and f2 represent, respectively, the lower and upper bounds of the range of frequencies to extract, while k is the approximation order to be used.
If these arguments are not supplied then the default values depend on the periodicity of the dataset. For yearly data the defaults for f1, f2 and k are 2, 8 and 3, respectively; for quarterly data, 6, 32 and 12; for monthly data, 18, 96 and 36. These values are chosen to match the most common choice among practitioners, that is to use this filter for extracting the "business cycle" frequency component; this, in turn, is commonly defined as being between 18 months and 8 years. The filter, per default choice, spans 3 years of data.
If f2 is greater than or equal to the number of available observations, then the "low-pass" version of the filter will be run and the resulting series should be taken as an estimate of the trend component, rather than the cycle. See also bwfilt, hpfilt.
Arguments: | y (series) |
d (scalar) |
Returns the Box–Cox transformation with parameter d for the positive series y.
The transformed series is (y^{d} - 1)/d for d not equal to zero, or log(y) for d = 0.
Arguments: | fname (string) |
import (boolean, optional) |
Reads a bundle from a text file. The string fname must contain the name of the file from which the bundle is to be read. If this name has the suffix ".gz" it is assumed that gzip compression has been applied in writing the file.
The file in question should be an appropriately defined XML file: it should contain a gretl-bundle element, which is used to store zero or more bundled-item elements. For example,
moo 3
As you may expect, such files are generated automatically by the companion function bwrite.
If the file name does not contain a full path specification, it will be looked for in several "likely" locations, beginning with the currently set workdir. However, if a non-zero value is given for the optional import argument, the input file is looked for in the user's "dot" directory. In this case the fname argument should be a plain filename, without any path component.
Should an error occur (such as the file being badly formatted or inaccessible), an error is returned via the $error accessor.
Arguments: | y (series) |
n (integer) | |
omega (scalar) |
Returns the result from application of a low-pass Butterworth filter with order n and frequency cutoff omega to the series y. The cutoff is expressed in degrees and must be greater than 0 and less than 180. Smaller cutoff values restrict the pass-band to lower frequencies and hence produce a smoother trend. Higher values of n produce a sharper cutoff, at the cost of possible numerical instability.
Inspecting the periodogram of the target series is a useful preliminary when you wish to apply this function. See chapter 24 of the Gretl User's Guide for details. See also bkfilt, hpfilt.
Arguments: | B (bundle) |
fname (string) | |
export (boolean, optional) |
Writes the bundle B to an XML file named fname. For a summary description of its format, see bread. If file fname already exists, it will be overwritten. The return value is 0 on successful completion; if an error occurs, such as the file being unwritable, the return value will be non-zero.
The output file will be written in the currently set workdir, unless the filename string contains a full path specification. However, if a non-zero value is given for the export argument, the output file will be written into the user's "dot" directory. In this case a plain filename, without any path component, should be given for the second argument.
Argument: | X (matrix) |
Centers the columns of matrix X around their means.
Arguments: | d (string) |
... (see below) | |
x (scalar, series or matrix) |
Cumulative distribution function calculator. Returns P(X <= x), where the distribution of X is determined by the string d. Between the arguments d and x, zero or more additional scalar arguments are required to specify the parameters of the distribution, as follows (but note that the normal distribution has its own convenience function, cnorm).
Standard normal (c = z, n, or N): no extra arguments
Bivariate normal (D): correlation coefficient
Student's t (t): degrees of freedom
Chi square (c, x, or X): degrees of freedom
Snedecor's F (f or F): df (num.); df (den.)
Gamma (g or G): shape; scale
Binomial (b or B): probability; number of trials
Poisson (p or P): Mean
Weibull (w or W): shape; scale
Generalized Error (E): shape
Non-central chi square (ncX): df, non-centrality parameter
Non-central F (ncF): df (num.), df (den.), non-centrality parameter
Non-central t (nct): df, non-centrality parameter
Note that most cases have aliases to help memorizing the codes. The bivariate normal case is special: the syntax is x = cdf(D, rho, z1, z2) where rho is the correlation between the variables z1 and z2.
See also pdf, critical, invcdf, pvalue.
Arguments: | X (matrix) |
Y (matrix) |
Complex division. The two arguments must have the same number of rows, n, and either one or two columns. The first column contains the real part and the second (if present) the imaginary part. The return value is an n x 2 matrix or, if the result has no imaginary part, an n-vector. See also cmult.
Argument: | x (scalar, series or matrix) |
Ceiling function: returns the smallest integer greater than or equal to x. See also floor, int.
Argument: | A (positive definite matrix) |
Peforms a Cholesky decomposition of the matrix A, which is assumed to be symmetric and positive definite. The result is a lower-triangular matrix L which satisfies A = LL'. The function will fail if A is not symmetric or not positive definite. See also psdroot.
Arguments: | Y (matrix) |
xfac (integer) | |
X (matrix, optional) |
Expands the input data, Y, to a higher frequency, using the interpolation method of Chow and Lin (1971). It is assumed that the columns of Y represent data series; the returned matrix has as many columns as Y and xfac times as many rows.
The second argument represents the expansion factor: it should be 3 for expansion from quarterly to monthly or 4 for expansion from annual to quarterly, these being the only supported factors. The optional third argument may be used to provide a matrix of covariates at the higher (target) frequency.
The regressors used by default are a constant and quadratic trend. If X is provided, its columns are used as additional regressors; it is an error if the number of rows in X does not equal xfac times the number of rows in Y.
Arguments: | X (matrix) |
Y (matrix) |
Complex multiplication. The two arguments must have the same number of rows, n, and either one or two columns. The first column contains the real part and the second (if present) the imaginary part. The return value is an n x 2 matrix, or, if the result has no imaginary part, an n-vector. See also cdiv.
Argument: | x (scalar, series or matrix) |
Returns the cumulative distribution function for a standard normal. See also dnorm, qnorm.
Arguments: | M (matrix) |
col (integer) |
Retrieves the name for column col of matrix M. If M has no column names attached the value returned is an empty string; if col is out of bounds for the given matrix an error is flagged. See also colnames.
Example:
matrix A = { 11, 23, 13 ; 54, 15, 46 } colnames(A, "Col_A Col_B Col_C") string name = colname(A, 3) print name
Arguments: | M (matrix) |
S (array of strings or list) |
Attaches names to the columns of the T x k matrix M. If S is a named list, the names are taken from the names of the listed series; the list must have k members. If S is an array of strings, it should contain k elements. For backward caompatibility, a single string may also be given as the second argument; in that case it should contain k space-separated substrings.
The return value is 0 on successful completion, non-zero on error. See also rownames.
Example:
matrix M = {1, 2; 2, 1; 4, 1} strings S = array(2) S[1] = "Col1" S[2] = "Col2" colnames(M, S) print M
Argument: | X (matrix) |
Returns the number of columns of X. See also mshape, rows, unvech, vec, vech.
Arguments: | y1 (series or vector) |
y2 (series or vector) |
Computes the correlation coefficient between y1 and y2. The arguments should be either two series, or two vectors of the same length. See also cov, mcov, mcorr.
Arguments: | x (series, matrix or list) |
p (integer) | |
y (series or vector, optional) |
If only the first two arguments are given, computes the correlogram for x for lags 1 to p. Let k represent the number of elements in x (1 if x is a series, the number of columns if x is a matrix, or the number of list-members is x is a list). The return value is a matrix with p rows and 2k columns, the first k columns holding the respective autocorrelations and the remainder the respective partial autocorrelations.
If a third argument is given, this function computes the cross-correlogram for each of the k elements in x and y, from lead p to lag p. The returned matrix has 2p + 1 rows and k columns. If x is series or list and y is a vector, the vector must have just as many rows as there are observations in the current sample range.
Argument: | x (scalar, series or matrix) |
Returns the cosine of x.
Argument: | x (scalar, series or matrix) |
Returns the hyperbolic cosine of x.
Arguments: | y1 (series or vector) |
y2 (series or vector) |
Returns the covariance between y1 and y2. The arguments should be either two series, or two vectors of the same length. See also corr, mcov, mcorr.
Arguments: | c (character) |
... (see below) | |
p (scalar, series or matrix) |
Critical value calculator. Returns x such that P(X > x) = p, where the distribution X is determined by the character c. Between the arguments c and p, zero or more additional scalar arguments are required to specify the parameters of the distribution, as follows.
Standard normal (c = z, n, or N): no extra arguments
Student's t (t): degrees of freedom
Chi square (c, x, or X): degrees of freedom
Snedecor's F (f or F): df (num.); df (den.)
Binomial (b or B): probability; trials
Poisson (p or P): mean
Argument: | x (series or matrix) |
Cumulates x (that is, creates a running sum). When x is a series, produces a series y each of whose elements is the sum of the values of x to date; the starting point of the summation is the first non-missing observation in the currently selected sample. When x is a matrix, its elements are cumulated by columns.
Argument: | &b (reference to bundle) |
Provides a somewhat flexible means of obtaining a text buffer containing data from an internet server, using libcurl. On input the bundle b must contain a string named URL which gives the full address of the resource on the target host. Other optional elements are as follows.
"header": a string specifying an HTTP header to be sent to the host.
"postdata": a string holding data to be sent to the host.
The header and postdata fields are intended for use with an HTTP POST request; if postdata is present the POST method is implicit, otherwise the GET method is implicit. (But note that for straightforward GET requests readfile offers a simpler interface.)
One other optional bundle element is recognized: if a scalar named include is present and has a non-zero value, this is taken as a request to include the header received from the host with the output body.
On completion of the request, the text received from the server is added to the bundle under the key "output".
If an error occurs in formulating the request (for example there's no URL on input) the function fails, otherwise it returns 0 if the request succeeds or non-zero if it fails, in which case the error message from the curl library is added to the bundle under the key "errmsg". Note, however, that "success" in this sense does not necessarily mean you got the data you wanted; all it means is that some response was received from the server. You must check the content of the output buffer (which may in fact be a message such as "Page not found").
Here is an example of use: downloading some data from the US Bureau of Labor Statistics site, which requires sending a JSON query. Note the use of sprintf to embed double-quotes in the POST data.
bundle req req.URL = "http://api.bls.gov/publicAPI/v1/timeseries/data/" req.include = 1 req.header = "Content-Type: application/json" string s = sprintf("{\"seriesid\":[\"LEU0254555900\"]}") req.postdata = s err = curl(&req) if err == 0 s = req.output string line loop while getline(s, line) --quiet printf "%s\n", line endloop endif
See also the jsonget function for means of processing JSON data received.
Argument: | ... (see below) |
Enables the definition of an array variable in extenso, by providing one or more elements. In using this function you must specify a type (in plural form) for the array: strings, matrices, bundles or lists. Each of the arguments must evaluate to an object of the specified type. On successful completion, the return value is an array of n elements, where n is the number of arguments.
strings S = defarray("foo", "bar", "baz") matrices M = defarray(I(3), X'X, A*B, P[1:])
Arguments: | x (series) |
c (character, optional) |
Depends on having TRAMO/SEATS or X-12-ARIMA installed. Returns a deseasonalized (seasonally adjusted) version of the input series x, which must be a quarterly or monthly time series. To use X-12-ARIMA give X as the second argument; to use TRAMO give T. If the second argument is omitted then X-12-ARIMA is used.
Note that if the input series has no detectable seasonal component this function will fail. Also note that both TRAMO/SEATS and X-12-ARIMA offer numerous options; deseas calls them with all options at their default settings. For both programs, the seasonal factors are calculated on the basis of an automatically selected ARIMA model. One difference between the programs which can sometimes make a substantial difference to the results is that by default TRAMO performs a prior adjustment for outliers while X-12-ARIMA does not.
Argument: | A (square matrix) |
Returns the determinant of A, computed via the LU factorization. See also ldet, rcond.
Argument: | X (matrix) |
Returns the principal diagonal of X in a column vector. Note: if X is an m x n matrix, the number of elements of the output vector is min(m, n). See also tr.
Arguments: | A (matrix) |
B (matrix) |
Returns the direct sum of A and B, that is a matrix holding A in its north-west corner and B in its south-east corner. If both A and B are square, the resulting matrix is block-diagonal.
Argument: | y (series, matrix or list) |
Computes first differences. If y is a series, or a list of series, starting values are set to NA. If y is a matrix, differencing is done by columns and starting values are set to 0.
When a list is returned, the individual variables are automatically named according to the template d_ varname where varname is the name of the original series. The name is truncated if necessary, and may be adjusted in case of non-uniqueness in the set of names thus constructed.
Argument: | x (scalar, series or matrix) |
Returns the digamma (or Psi) function of x, that is the derivative of the log of the Gamma function.
Argument: | x (scalar, series or matrix) |
Returns the density of the standard normal distribution at x. To get the density for a non-standard normal distribution at x, pass the z-score of x to the dnorm function and multiply the result by the Jacobian of the z transformation, namely 1 over σ, as illustrated below:
mu = 100 sigma = 5 x = 109 fx = (1/sigma) * dnorm((x-mu)/sigma)
Arguments: | X (list) |
epsilon (scalar, optional) |
Returns a list with the same elements as X, but for the collinear series. Therefore, if all the series in X are linearly independent, the output list is just a copy of X.
The algorithm uses the QR decomposition (Householder transformation), so it is subject to finite precision error. In order to gauge the sensitivity of the algorithm, a second optional parameter epsilon may be specified to make the collinearity test more or less strict, as desired. The default value for epsilon is 1.0e-8. Setting epsilon to a larger value increases the probability of a series to be dropped.
Example:
nulldata 20 set seed 9876 series foo = normal() series bar = normal() series foobar = foo + bar list X = foo bar foobar list Y = dropcoll(X) list print X list print Y # set epsilon to a ridiculously small value list Y = dropcoll(X, 1.0e-30) list print Y
produces
? list print X foo bar foobar ? list print Y foo bar ? list Y = dropcoll(X, 1.0e-30) Replaced list Y ? list print Y foo bar foobar
Argument: | x (series or vector) |
Sorts x in descending order, skipping observations with missing values when x is a series. See also sort, values.
Arguments: | x (series) |
omitval (scalar, optional) |
The argument x should be a discrete series. This function creates a set of dummy variables coding for the distinct values in the series. By default the smallest value is taken as the omitted category and is not explicitly represented.
The optional second argument represents the value of x which should be treated as the omitted category. The effect when a single argument is given is equivalent to dummify(x, min(x)). To produce a full set of dummies, with no omitted category, use dummify(x, NA).
The generated variables are automatically named according to the template Dvarname_i where varname is the name of the original series and i is a 1-based index. The original portion of the name is truncated if necessary, and may be adjusted in case of non-uniqueness in the set of names thus constructed.
Argument: | x (scalar, series or matrix) |
Given the year in argument x, returns the date of Easter in the Gregorian calendar as month + day/100. Note that April the 10th, is, under this convention, 4.1; hence, 4.2 is April the 20th, not April the 2nd (which would be 4.02).
scalar e = easterday(2014) scalar m = floor(e) scalar d = 100*(e-m)
Arguments: | A (square matrix) |
&U (reference to matrix, or null) |
Computes the eigenvalues, and optionally the right eigenvectors, of the n x n matrix A. If all the eigenvalues are real an n x 1 matrix is returned; otherwise the result is an n x 2 matrix, the first column holding the real components and the second column the imaginary components. The eigenvalues are not guaranteed to be sorted in any particular order.
The second argument must be either the name of an existing matrix preceded by & (to indicate the "address" of the matrix in question), in which case an auxiliary result is written to that matrix, or the keyword null, in which case the auxiliary result is not produced.
If a non-null second argument is given, the specified matrix will be over-written with the auxiliary result. (It is not required that the existing matrix be of the right dimensions to receive the result.) It will be organized as follows:
If the i-th eigenvalue is real, the i-th column of U will contain the corresponding eigenvector;
If the i-th eigenvalue is complex, the i-th column of U will contain the real part of the corresponding eigenvector and the next column the imaginary part. The eigenvector for the conjugate eigenvalue is the conjugate of the eigenvector.
In other words, the eigenvectors are stored in the same order as the eigenvalues, but the real eigenvectors occupy one column, whereas complex eigenvectors take two (the real part comes first); the total number of columns is still n, because the conjugate eigenvector is skipped.
See also eigensym, eigsolve, qrdecomp, svd.
Arguments: | A (symmetric matrix) |
&U (reference to matrix, or null) |
Works just as eigengen, but the argument A must be symmetric (in which case the calculations can be reduced). Unlike eigengen, eigenvalues are returned in ascending order.
Note: if you're interested in the eigen-decomposition of a matrix of the form X'X, where X is a large matrix, it is preferable to compute it via the prime operator X'X rather than using the more general syntax X'*X. The former expression uses a specialized algorithm which has the double advantage of being more efficient computationally and of ensuring that the result will be free by construction of machine precision artifacts that may render it numerically non-symmetric.
Arguments: | A (symmetric matrix) |
B (symmetric matrix) | |
&U (reference to matrix, or null) |
Solves the generalized eigenvalue problem |A – λB| = 0, where both A and B are symmetric and B is positive definite. The eigenvalues are returned directly, arranged in ascending order. If the optional third argument is given it should be the name of an existing matrix preceded by &; in that case the generalized eigenvectors are written to the named matrix.
Arguments: | year (scalar or series) |
month (scalar or series) | |
day (scalar or series) |
Returns the number of the day in the current epoch specified by year, month and day. The epoch day equals 1 for the first of January in the year 1 AD; it stood at 733786 on 2010-01-01. If any of the arguments are given as series the value returned is a series, otherwise it is a scalar.
For the inverse function, see isodate.
Argument: | errno (integer) |
Retrieves the gretl error message associated with errno. See also $error.
Argument: | name (string) |
Returns 1 if name is the identifier for a currently defined object, be it a scalar, a series, a matrix, list, string, bundle or array; otherwise returns 0.
Argument: | x (scalar, series or matrix) |
Returns e^{x}. Note that in case of matrices the function acts element by element. For the matrix exponential function, see mexp.
Arguments: | y (series or vector) |
f (series or vector) |
Produces a column vector holding several statistics which may be used for evaluating the series f as a forecast of the series y over the current sample range. Two vectors of the same length may be given in place of two series arguments.
The layout of the returned vector is as follows:
1 Mean Error (ME) 2 Mean Squared Error (MSE) 3 Mean Absolute Error (MAE) 4 Mean Percentage Error (MPE) 5 Mean Absolute Percentage Error (MAPE) 6 Theil's U 7 Bias proportion, UM 8 Regression proportion, UR 9 Disturbance proportion, UD
For details on the calculation of these statistics, and the interpretation of the U values, please see chapter 29 of the Gretl User's Guide.
Arguments: | b (column vector) |
fcall (function call) |
Calculates a numerical approximation to the Jacobian associated with the n-vector b and the transformation function specified by the argument fcall. The function call should take b as its first argument (either straight or in pointer form), followed by any additional arguments that may be needed, and it should return an m x 1 matrix. On successful completion fdjac returns an m x n matrix holding the Jacobian. Example:
matrix J = fdjac(theta, myfunc(&theta, X))
The function can use three different methods: simple forward-difference, bilateral difference or 4-nodes Richardson extrapolation. Respectively:
J_{0} = (f(x+h) - f(x))/h
J_{1} = (f(x+h) - f(x-h))/2h
J_{2} = [8(f(x+h) - f(x-h)) - (f(x+2h) - f(x-2h))] /12h
The three alternatives above provide, generally, a trade-off between accuracy and speed. You can choose among methods by using the set command and specify the value 0, 1 or 2 for the fdjac_quality variable.
For more details and examples see the chapter on numerical methods in chapter 31 of the Gretl User's Guide.
Argument: | X (matrix) |
Discrete real Fourier transform. If the input matrix X has n columns, the output has 2n columns, where the real parts are stored in the odd columns and the complex parts in the even ones.
Should it be necessary to compute the Fourier transform on several vectors with the same number of elements, it is numerically more efficient to group them into a matrix rather than invoking fft for each vector separately. See also ffti.
Argument: | X (matrix) |
Inverse discrete real Fourier transform. It is assumed that X contains n complex column vectors, with the real part in the odd columns and the imaginary part in the even ones, so the total number of columns should be 2n. A matrix with n columns is returned.
Should it be necessary to compute the inverse Fourier transform on several vectors with the same number of elements, it is numerically more efficient to group them into a matrix rather than invoking ffti for each vector separately. See also fft.
Arguments: | x (series or matrix) |
a (scalar or vector, optional) | |
b (scalar or vector, optional) | |
y0 (scalar, optional) |
Computes an ARMA-like filtering of the argument x. The transformation can be written as
y_{t} = a_{0} x_{t} + a_{1} x_{t-1} + ... a_{q} x_{t-q} + b_{1} y_{t-1} + ... b_{p}y_{t-p}
If argument x is a series, the result will be itself a series. Otherwise, if x is a matrix with T rows and k columns, the result will be a matrix of the same size, in which the filtering is performed column by column.
The two arguments a and b are optional. They may be scalars, vectors or the keyword null.
If a is a scalar, this is used as a_{0} and implies q=0; if it is a vector of q+1 elements, they contain the coefficients from a_{0} to a_{q}. If a is null or omitted, this is equivalent to setting a_{0} =1 and q=0.
If b is a scalar, this is used as b_{1} and implies p=1; if it is a vector of p elements, they contain the coefficients from b_{1} to b_{p}. If b is null or omitted, this is equivalent to setting B(L)=1.
The optional scalar argument y0 is taken to represent all values of y prior to the beginning of sample (used only when p>0). If omitted, it is understood to be 0. Pre-sample values of x are always assumed zero.
See also bkfilt, bwfilt, fracdiff, hpfilt, movavg, varsimul.
Example:
nulldata 5 y = filter(index, 0.5, -0.9, 1) print index y --byobs x = seq(1,5)' ~ (1 | zeros(4,1)) w = filter(x, 0.5, -0.9, 1) print x w
produces
index y 1 1 -0.40000 2 2 1.36000 3 3 0.27600 4 4 1.75160 5 5 0.92356 x (5 x 2) 1 1 2 0 3 0 4 0 5 0 w (5 x 2) -0.40000 -0.40000 1.3600 0.36000 0.27600 -0.32400 1.7516 0.29160 0.92356 -0.26244
Argument: | y (series) |
Returns the 1-based index of the first non-missing observation for the series y. Note that if some form of subsampling is in effect, the value returned may be smaller than the dollar variable $t1. See also lastobs.
Argument: | rawname (string) |
Intended for use in connection with the join command. Returns the result of converting rawname to a valid gretl identifier, which must start with a letter, contain nothing but (ASCII) letters, digits and the underscore character, and must not exceed 31 characters. The rules used in conversion are:
1. Skip any leading non-letters.
2. Until the 31-character limit is reached or the input is exhausted: transcribe "legal" characters; skip "illegal" characters apart from spaces; and replace one or more consecutive spaces with an underscore, unless the previous character transcribed is an underscore in which case space is skipped.
Argument: | y (scalar, series or matrix) |
Returns the greatest integer less than or equal to x. Note: int and floor differ in their effect for negative arguments: int(-3.5) gives –3, while floor(-3.5) gives –4.
Arguments: | y (series) |
d (scalar) |
Returns the fractional difference of order d for the series y.
Note that in theory fractional differentiation is an infinitely long filter. In practice, presample values of y_{t} are assumed to be zero.
A negative value of d can be given, in which case fractional integration is performed.
Argument: | x (scalar, series or matrix) |
Returns the gamma function of x.
Arguments: | varname (string) |
rhs (series) |
Provides the script writer with a convenient means of generating series whose names are not known in advance, and/or creating a series and appending it to a list in a single operation.
The first argument gives the name of the series to create (or modify); this can be a string literal, a string variable, or an expression that evaluates to a string. The second argument, rhs ("right-hand side"), defines the source series: this can be the name of an existing series or an expression that evaluates to a series, as would appear to the right of the equals sign when defining a series in the usual way.
The return value from this function is the ID number of the series in the dataset, a value suitable for inclusion in a list (or –1 on failure).
For example, suppose you want to add n random normal series to the dataset and put them all into a named list. The following will do the job:
list Normals = null loop i=1..n --quiet Normals += genseries(sprintf("norm%d", i), normal()) endloop
On completion Normals will contain the series norm1, norm2 and so on.
Argument: | s (string) |
If an environment variable by the name of s is defined, returns the string value of that variable, otherwise returns an empty string. See also ngetenv.
Arguments: | source (string) |
target (string) |
This function is used to read successive lines from source, which should be a named string variable. On each call a line from the source is written to target (which must also be a named string variable), with the newline character stripped off. The valued returned is 1 if there was anything to be read (including blank lines), 0 if the source has been exhausted.
Here is an example in which the content of a text file is broken into lines:
string s = readfile("data.txt") string line scalar i = 1 loop while getline(s, line) printf "line %d = '%s'\n", i++, line endloop
In this example we can be sure that the source is exhausted when the loop terminates. If the source might not be exhausted you should follow your regular call(s) to getline with a "clean up" call, in which target is replaced by null (or omitted altogether) as in
getline(s, line) # get a single line getline(s, null) # clean up
Note that although the reading position advances at each call to getline, source is not modified by this function, only target.
Arguments: | C (matrix) |
A (matrix) | |
B (matrix) | |
U (matrix) | |
&dP (reference to matrix, or null) |
Computes the GHK (Geweke, Hajivassiliou, Keane) approximation to the multivariate normal distribution function; see for example Geweke (1991). The value returned is an n x 1 vector of probabilities.
The argument C (m x m) should give the Cholesky factor (lower triangular) of the covariance matrix of m normal variates. The arguments A and B should both be n x m, giving respectively the lower and upper bounds applying to the variates at each of n observations. Where variates are unbounded, this should be indicated using the built-in constant $huge or its negative.
The matrix U should be m x r, with r the number of pseudo-random draws from the uniform distribution; suitable functions for creating U are muniform and halton.
We illustrate below with a relatively simple case where the multivariate probabilities can be calculated analytically. The series P and Q should be numerically very similar to one another, P being the "true" probability and Q its GHK approximation:
nulldata 20 series inf1 = -2*uniform() series sup1 = 2*uniform() series inf2 = -2*uniform() series sup2 = 2*uniform() scalar rho = 0.25 matrix V = {1, rho; rho, 1} series P = cdf(D, rho, inf1, inf2) - cdf(D, rho, sup1, inf2) \ - cdf(D, rho, inf1, sup2) + cdf(D, rho, sup1, sup2) C = cholesky(V) U = halton(2, 100) series Q = ghk(C, {inf1, inf2}, {sup1, sup2}, U)
The optional dP argument can be used to retrieve the n x k matrix of derivatives of the probabilities, where k equals 2m + m(m + 1)/2. The first m columns hold the derivatives with respect to the lower bounds, the next m those with respect to the upper bounds, and the remainder the derivatives with respect to the unique elements of the C matrix in "vech" order.
Argument: | y (series) |
Returns Gini's inequality index for the series y.
Argument: | A (matrix) |
Returns A^{+}, the Moore–Penrose or generalized inverse of A, computed via the singular value decomposition.
This matrix has the properties A A^{+} A = A and A^{+} A A^{+} = A^{+}. Moreover, the products A A^{+} and A^{+} A are symmetric by construction.
Arguments: | m (integer) |
r (integer) | |
offset (integer, optional) |
Returns an m x r matrix containing m Halton sequences of length r; m is limited to a maximum of 40. The sequences are contructed using the first m primes. By default the first 10 elements of each sequence are discarded, but this figure can be adjusted via the optional offset argument, which should be a non-negative integer. See Halton and Smith (1964).
Arguments: | X (matrix) |
Y (matrix) |
Horizontal direct product. The two arguments must have the same number of rows, r. The return value is a matrix with r rows, in which the i-th row is the Kronecker product of the corresponding rows of X and Y.
This operation is called "horizontal direct product" in conformity to its implementation in the GAUSS programming language. Its equivalent in standard matrix algebra would be called the row-wise Khatri-Rao product.
Example: the code
A = {1,2,3; 4,5,6} B = {0,1; -1,1} C = hdprod(A, B)
produces the following matrix:
0 1 0 2 0 3 -4 4 -5 5 -6 6
Arguments: | hfvars (list) |
multiplier (scalar) |
Given a MIDAS list, produces a list of the same length holding high-frequency first differences. The second argument is optional and defaults to unity: it can be used to multiply the differences by some constant.
Arguments: | hfvars (list) |
multiplier (scalar) |
Given a MIDAS list, produces a list of the same length holding high-frequency log-differences. The second argument is optional and defaults to unity: it can be used to multiply the differences by some constant, for example one might give a value of 100 to produce (approximate) percentage changes.
Arguments: | minlag (integer) |
maxlag (integer) | |
hfvars (list) |
Given a MIDAS list, hfvars, produces a list holding high-frequency lags minlag to maxlag. Use positive values for actual lags, negative for leads. For example, if minlag is –3 and maxlag is 5 than the returned list will hold 9 series: 3 leads, the contemporary value, and 5 lags.
Note that high-frequency lag 0 corresponds to the first high frequency period within a low frequency period, for example the first month of a quarter or the first day of a month.
Arguments: | x (vector) |
m (integer) | |
prefix (string) |
Produces from the vector x a MIDAS list of m series, where m is the ratio of the frequency of observation for the variable in x to the base frequency of the current dataset. The value of m must be at least 3 and the length of x must be m times the length of the current sample range.
The names of the series in the returned list are constructed from the given prefix (which must be an ASCII string of 24 characters or less, and valid as a gretl identifier), plus one or more digits representing the sub-period of the observation. An error is flagged if any of these names duplicate names of existing objects.
Arguments: | y (series) |
lambda (scalar, optional) |
Returns the cycle component from application of the Hodrick–Prescott filter to series y. If the smoothing parameter, lambda, is not supplied then a data-based default is used, namely 100 times the square of the periodicity (100 for annual data, 1600 for quarterly data, and so on). See also bkfilt, bwfilt.
Argument: | n (integer) |
Returns an identity matrix with n rows and columns.
Argument: | X (matrix) |
Returns the row indices of the maxima of the columns of X.
Argument: | X (matrix) |
Returns the column indices of the maxima of the rows of X.
Arguments: | M (matrix) |
x (scalar) |
Computes Prob(u'Au < x) for a quadratic form in standard normal variates, u, using the procedure developed by Imhof (1961).
If the first argument, M, is a square matrix it is taken to specify A, otherwise if it's a column vector it is taken to be the precomputed eigenvalues of A, otherwise an error is flagged.
See also pvalue.
Argument: | X (matrix) |
Returns the row indices of the minima of the columns of X.
Argument: | X (matrix) |
Returns the column indices of the mimima of the rows of X.
Arguments: | b (bundle) |
key (string) |
Checks whether bundle b contains a data-item with name key. The value returned is an integer code for the type of the item: 0 for no match, 1 for scalar, 2 for series, 3 for matrix, 4 for string, 5 for bundle and 6 for array. The function typestr may be used to get the string corresponding to this code.
Argument: | X (matrix) |
Returns the infinity-norm of X, that is, the maximum across the rows of X of the sum of absolute values of the row elements.
Arguments: | L (list) |
y (series) |
Returns the (1-based) position of y in list L, or 0 if y is not present in L. The second argument may be given as the name of a series or alternatively as an integer ID number.
Argument: | x (scalar, series or matrix) |
Returns the integer part of x, truncating the fractional part. Note: int and floor differ in their effect for negative arguments: int(-3.5) gives –3, while floor(-3.5) gives –4. See also ceil.
Argument: | A (square matrix) |
Returns the inverse of A. If A is singular or not square, an error message is produced and nothing is returned. Note that gretl checks automatically the structure of A and uses the most efficient numerical procedure to perform the inversion.
The matrix types gretl checks for are: identity; diagonal; symmetric and positive definite; symmetric but not positive definite; and triangular.
Note: it makes sense to use this function only if you plan to use the inverse of A more than once. If you just need to compute an expression of the form A^{-1}B, you'll be much better off using the "division" operators \ and /. See chapter 15 of the Gretl User's Guide for details.
Arguments: | d (string) |
... (see below) | |
p (scalar, series or matrix) |
Inverse cumulative distribution function calculator. Returns x such that P(X <= x) = p, where the distribution of X is determined by the string d. Between the arguments d and p, zero or more additional scalar arguments are required to specify the parameters of the distribution, as follows.
Standard normal (c = z, n, or N): no extra arguments
Gamma (g or G): shape; scale
Student's t (t): degrees of freedom
Chi square (c, x, or X): degrees of freedom
Snedecor's F (f or F): df (num.); df (den.)
Binomial (b or B): probability; trials
Poisson (p or P): mean
Standardized GED (E): shape
Non-central chi square (ncX): df, non-centrality parameter
Non-central F (ncF): df (num.), df (den.), non-centrality parameter
Non-central t (nct): df, non-centrality parameter
See also cdf, critical, pvalue.
Argument: | x (scalar, series or matrix) |
Returns the inverse Mills ratio at x, that is the ratio between the standard normal density and the complement to the standard normal distribution function, both evaluated at x.
This function uses a dedicated algorithm which yields greater accuracy compared to calculation using dnorm and cnorm, but the difference between the two methods is appreciable only for very large negative values of x.
Argument: | A (positive definite matrix) |
Returns the inverse of the symmetric, positive definite matrix A. This function is slightly faster than inv for large matrices, since no check for symmetry is performed; for that reason it should be used with care.
Note: if you're interested in the inversion of a matrix of the form X'X, where X is a large matrix, it is preferable to compute it via the prime operator X'X rather than using the more general syntax X'*X. The former expression uses a specialized algorithm which has the double advantage of being more efficient computationally and of ensuring that the result will be free by construction of machine precision artifacts that may render it numerically non-symmetric.
Arguments: | target (integer) |
shock (integer) | |
alpha (scalar between 0 and 1, optional) |
This function is available only when the last model estimated was a VAR or VECM. It returns a matrix containing the estimated response of the target variable to an impulse of one standard deviation in the shock variable. These variables are identified by their position in the VAR specification: for example, if target and shock are given as 1 and 3 respectively, the returned matrix gives the response of the first variable in the VAR for a shock to the third variable.
If the optional alpha argument is given, the returned matrix has three columns: the point estimate of the responses, followed by the lower and upper limits of a 1 – α confidence interval obtained via bootstrapping. (So alpha = 0.1 corresponds to 90 percent confidence.) If alpha is omitted or set to zero, only the point estimate is provided.
The number of periods (rows) over which the response is traced is determined automatically based on the frequency of the data, but this can be overridden via the set command, as in set horizon 10.
Argument: | x (series or vector) |
Returns the Internal Rate of Return for x, considered as a sequence of payments (negative) and receipts (positive). See also npv.
Arguments: | y (series or vector) |
panel-code (integer, optional) |
Without the optional second argument, returns 1 if y has a constant value over the current sample range (or over its entire length if y is a vector), otherwise 0.
The second argument is accepted only if the current dataset is a panel and y is a series. In that case a panel-code value of 0 calls for a check for time-invariance, while a value of 1 means check for cross-sectional invariance (that is, in each time period the value of y is the same for all groups).
If y is a series, missing values are ignored in checking for constancy.
Argument: | name (string) |
If name is the identifier for a currently defined series, returns 1 if the series is marked as discrete-valued, otherwise 0. If name does not identify a series, returns NA.
Argument: | x (series or vector) |
If all the values contained in x are 0 or 1 (or missing), returns the number of ones, otherwise 0.
Argument: | x (scalar or matrix) |
Given a scalar argument, returns 1 if x is "Not a Number" (NaN), otherwise 0. Given a matrix argument, returns a matrix of the same dimensions with 1s in positions where the corresponding element of the input is NaN and 0s elsewhere.
Argument: | name (string) |
Returns 0 if name is the identifier for a currently defined object, be it a scalar, a series, a matrix, list, string or bundle; otherwise returns 1.
This function is deprecated: the recommended replacment is (the negation of) exists.
Arguments: | date (series) |
&year (reference to series) | |
&month (reference to series) | |
&day (reference to series, optional) |
Given a series date holding dates in ISO 8601 "basic" format (YYYYMMDD), this function writes the year, month and (optionally) day components into the series named by the second and subsequent arguments. An example call, assuming the series dates contains suitable 8-digit values:
series y, m, d isoconv(dates, &y, &m, &d)
The return value from this function is 0 on successful completion, non-zero on error.
Arguments: | ed (scalar or series) |
as-string (boolean, optional) |
The argument ed is interpreted as an epoch day (which equals 1 for the first of January in the year 1 AD). The default return value — of the same type as ed — is an 8-digit number, or a series of such numbers, on the pattern YYYYMMDD (ISO 8601 "basic" format), giving the calendar date corresponding to the epoch day.
If ed is a scalar (only) and the optional second argument as-string is non-zero, the return value is not numeric but rather a string on the pattern YYYY-MM-DD (ISO 8601 "extended" format).
For the inverse function, see epochday.
Arguments: | S (symmetric matrix) |
v (integer) |
Given S (a positive definite p x p scale matrix), returns a drawing from the Inverse Wishart distribution with v degrees of freedom. The returned matrix is also p x p. The algorithm of Odell and Feiveson (1966) is used.
Arguments: | buf (string) |
path (string) |
The argument buf should be a JSON buffer, as may be retrieved from a suitable website via the curl function, and the path argument should be a JsonPath specification.
This function returns a string representing the data found in the buffer at the specified path. Data types of double (floating-point), int (integer) and string are supported. In the case of doubles or ints, their string representation is returned (using the "C" locale for doubles). If the object to which path refers is an array, the members are printed one per line in the returned string.
An accurate account of JsonPath syntax can be found at http://goessner.net/articles/JsonPath/. However, please note that the back-end for jsonget is provided by json-glib, which does not necessarily support all elements of JsonPath. Moreover, the exact functionality of json-glib may differ depending on the version you have on your system. See http://developer.gnome.org/json-glib/ if you need details.
That said, the following operators should be available to jsonget:
root node, via the $ character
recursive descent operator: ..
wildcard operator: *
subscript operator: []
set notation operator, for example [i,j]
slice operator: [start:end:step]
Arguments: | x (series or vector) |
scale (scalar, optional) | |
control (boolean, optional) |
Computes a kernel density estimate for the series or vector x. The returned matrix has two columns, the first holding a set of evenly spaced abscissae and the second the estimated density at each of these points.
The optional scale parameter can be used to adjust the degree of smoothing relative to the default of 1.0 (higher values produce a smoother result). The control parameter acts as a boolean: 0 (the default) means that the Gaussian kernel is used; a non-zero value switches to the Epanechnikov kernel.
A plot of the results may be obtained using the gnuplot command, as in
matrix d = kdensity(x) gnuplot 2 1 --matrix=d --with-lines --suppress-fitted
Arguments: | &Mod (reference to bundle) |
MSE (boolean, optional) |
Performs disturbance smoothing for a Kalman bundle previously set up by means of ksetup and returns 0 on successful completion or 1 if numerical problems are encountered.
On successful completion, the smoothed disturbances will be available as Mod.smdist.
The optional MSE argument determines the contents of the Mod.smdisterr key. If 0 or omitted, this matrix will contain the unconditional standard errors of the smoothed residuals, which are normally used to compute the so-called auxiliary residuals. Otherwise, Mod.smdisterr will contain the estimated root mean square deviations of the auxiliary residuals from their true value.
For more details see chapter 30 of the Gretl User's Guide.
See also ksetup, kfilter, ksmooth, ksimul.
Argument: | &Mod (reference to bundle) |
Performs a forward, filtering pass on a Kalman bundle previously set up by means of ksetup and returns 0 on successful completion or 1 if numerical problems are encountered.
On successful completion, the one-step-ahead prediction errors will be available as Mod.prederr and the sequence of their covariance matrices as Mod.pevar. Moreover, the key Mod.llt gives access to a T-vector containing the log-likelihood by observation.
For more details see chapter 30 of the Gretl User's Guide.
See also kdsmooth, ksetup, ksmooth, ksimul.
Arguments: | T (scalar) |
trend (boolean) |
Returns a row vector containing critical values at the 10, 5 and 1 percent levels for the KPSS test for stationarity of a time series. T should give the number of observations and trend should be 1 if the test includes a trend, 0 otherwise.
The critical values given are based on response surfaces estimated in the manner set out by Sephton (Economics Letters, 1995). See also the kpss command.
Arguments: | Y (series, matrix or list) |
H (scalar or matrix) | |
F (scalar or matrix) | |
Q (scalar or matrix) | |
C (matrix, optional) |
Sets up a Kalman bundle, that is an object which contains all the information needed to define a linear state space model of the form
and state transition equation
where Var(u) = Q.
Objects created via this function can be later used via the dedicated functions kfilter for filtering, ksmooth and kdsmooth for smoothing and ksimul for performing simulations.
The class of models that gretl can handle is in fact much wider than the one implied by the representation above: it is possible to have time-varying models, models with diffuse priors and exogenous variable in the measurement equation and models with cross-correlated innovations. For further details, see chapter 30 of the Gretl User's Guide.
See also kdsmooth, kfilter, ksmooth, ksimul.
Argument: | &Mod (reference to bundle) |
Uses a Kalman bundle previously set up by means of ksetup to simulate data.
For details see chapter 30 of the Gretl User's Guide.
See also ksetup, kfilter, ksmooth.
Argument: | &Mod (reference to bundle) |
Performs a fixed-point smoothing (backward) pass on a Kalman bundle previously set up by means of ksetup and returns 0 on successful completion or 1 if numerical problems are encountered.
On successful completion, the smoothed states will be available as Mod.state and the sequence of their covariance matrices as Mod.stvar. For more details see chapter 30 of the Gretl User's Guide.
See also ksetup, kdsmooth, kfilter, ksimul.
Argument: | x (series) |
Returns the excess kurtosis of the series x, skipping any missing observations.
Arguments: | p (scalar or vector) |
y (series or list) | |
bylag (boolean, optional) |
If the first argument is a scalar, generates lags 1 to p of the series y, or if y is a list, of all series in the list. If p = 0, the maximum lag defaults to the periodicity of the data; otherwise p must be positive.
If a vector is given as the first argument, the lags generated are those specified in the vector. Common usage in this case would be to give p as, for example, seq(3,7), hence omitting the first and second lags. However, it is OK to give a vector with gaps, as in {3,5,7}, although the lags should always be given is ascending order.
The generated variables are automatically named according to the template varname _ i where varname is the name of the original series and i is the specific lag. The original portion of the name is truncated if necessary, and may be adjusted in case of non-uniqueness in the set of names thus constructed.
When y is a list and the lag order is greater than 1, the default ordering of the terms in the returned list is by variable: all lags of the first series in the input list followed by all lags of the second series, and so on. The optional third argument can be used to change this: if bylag is non-zero then the terms are ordered by lag: lag 1 of all the input series, then lag 2 of all the series, and so on.
Argument: | y (series) |
Returns the 1-based index of the last non-missing observation for the series y. Note that if some form of subsampling is in effect, the value returned may be larger than the dollar variable $t2. See also firstobs.
Argument: | A (square matrix) |
Returns the natural log of the determinant of A, computed via the LU factorization. See also det, rcond.
Argument: | y (series or list) |
Computes log differences; starting values are set to NA.
When a list is returned, the individual variables are automatically named according to the template ld_varname where varname is the name of the original series. The name is truncated if necessary, and may be adjusted in case of non-uniqueness in the set of names thus constructed.
Arguments: | L (list) |
b (vector) |
Computes a new series as a linear combination of the series in the list L. The coefficients are given by the vector b, which must have length equal to the number of series in L.
Argument: | x (series) |
Depends on having TRAMO installed. Returns a "linearized" version of the input series; that is, a series in which any missing values are replaced by interpolated values and outliers are adjusted. TRAMO's fully automatic mechanism is used; consult the TRAMO documentation for details.
Note that if the input series has no missing values and no values that TRAMO regards as outliers, this function will return a copy of the original series.
Arguments: | y (series) |
p (integer) |
Computes the Ljung–Box Q' statistic for the series y using lag order p, over the currently defined sample range. The lag order must be greater than or equal to 1 and less than the number of available observations.
This statistic may be referred to the chi-square distribution with p degrees of freedom as a test of the null hypothesis that the series y is not serially correlated. See also pvalue.
Argument: | x (scalar, series or matrix) |
Returns the log of the gamma function of x.
Argument: | x (scalar, series, matrix or list) |
Returns the natural logarithm of x; produces NA for non-positive values. Note: ln is an acceptable alias for log.
When a list is returned, the individual variables are automatically named according to the template l_varname where varname is the name of the original series. The name is truncated if necessary, and may be adjusted in case of non-uniqueness in the set of names thus constructed.
Argument: | x (scalar, series or matrix) |
Returns the base-10 logarithm of x; produces NA for non-positive values.
Argument: | x (scalar, series or matrix) |
Returns the base-2 logarithm of x; produces NA for non-positive values.
Arguments: | y (series) |
x (series) | |
d (integer, optional) | |
q (scalar, optional) | |
robust (boolean, optional) |
Performs locally-weighted polynomial regression and returns a series holding predicted values of y for each non-missing value of x. The method is as described by William Cleveland (1979).
The optional arguments d and q specify the order of the polynomial in x and the proportion of the data points to be used in local estimation, respectively. The default values are d = 1 and q = 0.5. The other acceptable values for d are 0 and 2. Setting d = 0 reduces the local regression to a form of moving average. The value of q must be greater than 0 and cannot exceed 1; larger values produce a smoother outcome.
If a non-zero value is given for the robust argument the local regressions are iterated twice, with the weights being modified based on the residuals from the previous iteration so as to give less influence to outliers.
See also nadarwat, and in addition see chapter 34 of the Gretl User's Guide for details on nonparametric methods.
Argument: | x (scalar, series or matrix) |
Returns the logistic function of the argument x, that is, e^{x}/(1 + e^{x}). If x is a matrix, the function is applied element by element.
Argument: | A (matrix) |
Returns an n x n lower triangular matrix: the elements on and below the diagonal are equal to the corresponding elements of A; the remaining elements are zero.
Arguments: | y (series or vector) |
k (integer) |
Returns the long-run variance of y, calculated using a Bartlett kernel with window size k. The default window size, namely the integer part of the cube root of the sample size, can be selected by giving a negative value for k.
Argument: | y (series or list) |
If the argument y is a series, returns the (scalar) maximum of the non-missing observations in the series. If the argument is a list, returns a series each of whose elements is the maximum of the values of the listed variables at the given observation.
Argument: | X (matrix) |
Returns a row vector containing the maxima of the columns of X.
Argument: | X (matrix) |
Returns a column vector containing the maxima of the rows of X.
Argument: | X (matrix) |
Computes a correlation matrix treating each column of X as a variable. See also corr, cov, mcov.
Argument: | X (matrix) |
Computes a covariance matrix treating each column of X as a variable. See also corr, cov, mcorr.
Arguments: | X (matrix) |
u (vector, optional) | |
w (vector, optional) | |
p (integer) |
Returns the matrix covariogram for a T x k matrix X (typically containing regressors), an (optional) T -vector u (typically containing residuals), an (optional) (p+1)-vector of weights w, and a lag order p, which must be greater than or equal to 0.
The returned matrix is given by
sum_{j=-p}^p sum_j w_{|j|} (X_t' u_t u_{t-j} X_{t-j})
If u is given as null the u terms are omitted, and if w is given as null all the weights are taken to be 1.0.
Argument: | x (series or list) |
If x is a series, returns the (scalar) sample mean, skipping any missing observations.
If x is a list, returns a series y such that y_{t} is the mean of the values of the variables in the list at observation t, or NA if there are any missing values at t.
Argument: | X (matrix) |
Returns the means of the columns of X. See also meanr, sumc, sdc.
Argument: | X (matrix) |
Returns the means of the rows of X. See also meanc, sumr.
Argument: | y (series) |
The median of the non-missing observations in series y. See also quantile.
Argument: | A (square matrix) |
Computes the matrix exponential of A, using algorithm 11.3.1 from Golub and Van Loan (1996).
Arguments: | p (integer) |
theta (vector) | |
type (integer) |
Let k denote the number of elements in the vector of hyper-parameters, theta. This function returns a p x k matrix holding the gradient of the vector of weights (as calculated by mweights) with respect to the elements of theta. The first argument represents the desired lag order and the last argument specifies the type of parameterization. See mweights for an account of the acceptable type values.
Argument: | y (series or list) |
If the argument y is a series, returns the (scalar) minimum of the non-missing observations in the series. If the argument is a list, returns a series each of whose elements is the minimum of the values of the listed variables at the given observation.
Argument: | X (matrix) |
Returns the minima of the columns of X.
Argument: | X (matrix) |
Returns the minima of the rows of X.
Argument: | x (scalar, series or list) |
Returns a binary variable holding 1 if x is NA. If x is a series, the comparison is done element by element; if x is a list of series, the output is a series with 1 at observations for which at least one series in the list has a missing value, and 0 otherwise.
See also misszero, ok, zeromiss.
Argument: | x (scalar or series) |
Converts NAs to zeros. If x is a series, the conversion is done element by element. See also missing, ok, zeromiss.
Arguments: | X (matrix) |
p (scalar or vector) | |
m (scalar, optional) |
Shifts up or down the rows of X. If p is a positive scalar, returns a matrix in which the columns of X are shifted down by p rows and the first p rows are filled with the value m. If p is a negative number, X is shifted up and the last rows are filled with the value m. If m is omitted, it is understood to be zero.
If p is a vector, the above operation is carried out for each element in p, joining the resulting matrices horizontally.
Arguments: | hfvars (list) |
theta (vector) | |
type (integer) |
A convenience MIDAS function which combines lincomb with mweights. Given a list hfvars, it constructs a series which is a weighted sum of the elements of the list, the weights based on the vector of hyper-parameters theta and the type of parameterization: see mweights for details. Note that hflags is generally the best way to create a list suitable as the first argument to this function.
To be explicit, the call
series s = mlincomb(hfvars, theta, 2)
is equivalent to
matrix w = mweights(nelem(hfvars), theta, 2) series s = lincomb(hfvars, w)
but use of mlincomb saves on some typing and also some CPU cycles.
Arguments: | r (integer) |
c (integer) |
Returns a matrix with r rows and c columns, filled with standard normal pseudo-random variates. See also normal, muniform.
Arguments: | Y (matrix) |
X (matrix) | |
&U (reference to matrix, or null) | |
&V (reference to matrix, or null) |
Returns a k x n matrix of parameter estimates obtained by OLS regression of the T x n matrix Y on the T x k matrix X.
If the third argument is not null, the T x n matrix U will contain the residuals. If the final argument is given and is not null then the k x k matrix V will contain (a) the covariance matrix of the parameter estimates, if Y has just one column, or (b) X'X^{-1} if Y has multiple columns.
By default, estimates are obtained via Cholesky decomposition, with a fallback to QR decomposition if the columns of X are highly collinear. The use of SVD can be forced via the command set svd on.
Arguments: | month (integer) |
year (integer) | |
weeklen (integer) |
Returns the number of (relevant) days in the specified month in the specified year; weeklen, which must equal 5, 6 or 7, gives the number of days in the week that should be counted (a value of 6 omits Sundays, and a value of 5 omits both Saturdays and Sundays).
Arguments: | x (series) |
p (scalar) | |
control (integer, optional) | |
y0 (scalar, optional) |
Depending on the value of the parameter p, returns either a simple or an exponentially weighted moving average of the input series x.
If p > 1, a simple p-term moving average is computed, that is, the arithmetic mean of x from period t to t-p+1. If a non-zero value is supplied for the optional control parameter the MA is centered, otherwise it is "trailing". The optional y0 argument is ignored.
If p is a positive fraction, an exponential moving average is computed:
y(t) = p*x(t) + (1-p)*y(t-1)
By default the output series, y, is initialized using the first value of x, but the control parameter may be used to specify the number of initial observations that should be averaged to produce y(0). A zero value for control indicates that all the observations should be used. Alternatively, an initializer may be specified using the optional y0 argument; in that case the control argument is ignored.
Arguments: | Y (matrix) |
X (matrix) | |
&U (reference to matrix, or null) |
Works exactly as mols, except that the calculations are done in multiple precision using the GMP library.
By default GMP uses 256 bits for each floating point number, but you can adjust this using the environment variable GRETL_MP_BITS, e.g. GRETL_MP_BITS=1024.
Arguments: | d (string) |
p1 (scalar) | |
p2 (scalar, conditional) | |
p3 (scalar, conditional) | |
rows (integer) | |
cols (integer) |
Works like randgen except that the return value is a matrix rather than a series. The initial arguments to this function (the number of which depends on the selected distribution) are as described for randgen, but they must be followed by two integers to specify the number of rows and columns of the desired random matrix.
The first example above calls for a uniform random column vector of length 50, while the second example specifies a 20 x 20 random matrix with drawings from the t distribution with 14 degrees of freedom.
Arguments: | fname (string) |
import (boolean, optional) |
Reads a matrix from a file named fname. If the filename has the suffix ".gz" it is assumed that gzip compression has been applied in writing the data; if it has the suffix ".bin" the file is assumed to be in binary format (see mwrite for details). Otherwise the file is assumed to be plain text, conforming to the following specification:
It may start with any number of comments, defined as lines that start with the hash mark, #; such lines are ignored.
The first non-comment line must contain two integers, separated by a space or a tab, indicating the number of rows and columns, respectively.
The columns must be separated by spaces or tab characters.
The decimal separator must be the dot character, ".".
If the file name does not contain a full path specification, it will be looked for in several "likely" locations, beginning with the currently set workdir. However, if a non-zero value is given for the optional import argument, the input file is looked for in the user's "dot" directory. This is intended for use with the matrix-exporting functions offered in the context of the foreign command. In this case the fname argument should be a plain filename, without any path component.
Argument: | X (matrix) |
Returns a matrix containing the rows of X in reverse order. If you wish to obtain a matrix in which the columns of X appear in reverse order you can do:
matrix Y = mreverse(X')'
Arguments: | Y (matrix) |
X (matrix) | |
R (matrix) | |
q (column vector) | |
&U (reference to matrix, or null) | |
&V (reference to matrix, or null) |
Restricted least squares: returns a k x n matrix of parameter estimates obtained by least-squares regression of the T x n matrix Y on the T x k matrix X subject to the linear restriction RB = q, where B denotes the stacked coefficient vector. R must have kn columns; each row of this matrix represents a linear restriction. The number of rows in q must match the number of rows in R.
If the fifth argument is not null, the T x n matrix U will contain the residuals. If the final argument is given and is not null then the k x k matrix V will hold the restricted counterpart to the matrix X'X^{-1}. The variance matrix of the estimates for equation i can be constructed by multiplying the appropriate sub-matrix of V by an estimate of the error variance for that equation.
Arguments: | X (matrix) |
r (integer) | |
c (integer) |
Rearranges the elements of X into a matrix with r rows and c columns. Elements are read from X and written to the target in column-major order. If X contains fewer than k = rc elements, the elements are repeated cyclically; otherwise, if X has more elements, only the first k are used.
See also cols, rows, unvech, vec, vech.
Arguments: | X (matrix) |
j (integer) |
Returns a matrix in which the rows of X are reordered by increasing value of the elements in column j. This is a stable sort: rows that share the same value in column j will not be interchanged.
Arguments: | r (integer) |
c (integer) |
Returns a matrix with r rows and c columns, filled with uniform (0,1) pseudo-random variates. Note: the preferred method for generating a scalar uniform r.v. is to use the randgen1 function.
Arguments: | p (integer) |
theta (vector) | |
type (integer) |
Returns a p-vector of MIDAS weights to be applied to p lags of a high-frequency series, based on the vector theta of hyper-parameters.
The type argument identifies the type of parameterization, which governs the required number of elements, k, in theta: 1 = normalized exponential Almon (k at least 1, typically 2); 2 = normalized beta with zero last (k = 2); 3 = normalized beta with non-zero last lag (k = 3); and 4 = Almon polynomial (k at least 1).
Arguments: | X (matrix) |
fname (string) | |
export (boolean, optional) |
Writes the matrix X to a file named fname. By default this file will be plain text; the first line will hold two integers, separated by a tab character, representing the number of rows and columns; on the following lines the matrix elements appear, in scientific notation, separated by tabs (one line per row). See below for alternative formats.
If a file fname already exists, it will be overwritten. The return value is 0 on successful completion; if an error occurs, such as the file being unwritable, the return value will be non-zero.
The output file will be written in the currently set workdir, unless the filename string contains a full path specification. However, if a non-zero value is given for the export argument, the output file will be written into the user's "dot" directory, where it is accessible by default via the matrix-loading functions offered in the context of the foreign command. In this case a plain filename, without any path component, should be given for the second argument.
Matrices stored via the mwrite function in its default form can be easily read by other programs; see chapter 15 of the Gretl User's Guide for details.
Two mutually exclusive inflections of this function are available, as follows:
If fname has the suffix ".gz" the the file is written with gzip compression. The format is basically as described above except that the matrix elements are written in a single column, in column-major order.
If fname has the suffix ".bin" the the file is written in binary format. In this case the first 19 bytes contain the characters gretl_binary_matrix, the next 8 bytes contain two 32-bit integers giving the number of rows and columns, and the remainder of the file contains the matrix elements as little-endian "doubles", in column-major order. If gretl is run on a big-endian system, the binary values are converted to little endian on writing, and converted to big endian on reading.
Note that if the matrix file is to be read by a third-party program it is not advisable to use the gzip or binary options. But if the file is intended for reading by gretl the alternative formats save space, and the binary format allows for much faster reading of large matrices.
See also mread.
Arguments: | x (series or vector) |
y (series or vector) |
Returns a matrix holding the cross tabulation of the values contained in x (by row) and y (by column). The two arguments should be of the same type (both series or both column vectors), and because of the typical usage of this function, are assumed to contain integer values only.
Arguments: | y (series) |
x (series) | |
h (scalar) |
Returns the Nadaraya–Watson nonparametric estimator of the conditional mean of y given x. It returns a series holding the nonparametric estimate of E(y_{i}|x_{i}) for each nonmissing element of the series x.
The kernel function K is given by K = exp(-x^{2} / 2h) for |x| < T and zero otherwise.
The argument h, known as the bandwidth, is a parameter (a positive real number) given by the user. This is usually a small number: larger values of h make m(x) smoother; a popular choice is n^{-0.2}. More details are given in chapter 34 of the Gretl User's Guide.
The scalar T is used to prevent numerical problems when the kernel function is evaluated too far away from zero and is called the trim parameter.
The trim parameter can be adjusted via the nadarwat_trim setting, as a multiple of h. The default value is 4.
The user may provide a negative value for the bandwidth: this is interpreted as conventional syntax to obtain the leave-one-out estimator, that is a variant of the estimator that does not use the i-th observation for evaluating m(x_{i}). This makes the Nadaraya–Watson estimator more robust numerically and its usage is normally advised when the estimator is computed for inference purposes. Of course, the bandwidth actually used is the absolute value of h.
Argument: | L (list, matrix, bundle or array) |
Returns the number of elements in the argument, which may be a list, a matrix, a bundle, or an array (but not a series).
Argument: | s (string) |
If an environment variable by the name of s is defined and has a numerical value, returns that value; otherwise returns NA. See also getenv.
Argument: | buf (string) |
Returns a count of the complete lines (that is, lines that end with the newline character) in buf.
Example:
string web_page = readfile("http://gretl.sourceforge.net/") scalar number = nlines(web_page) print number
Argument: | y (series) |
Returns the number of non-missing observations for the variable y in the currently selected sample.
Arguments: | μ (scalar) |
σ (scalar) |
Generates a series of Gaussian pseudo-random variates with mean μ and standard deviation σ. If no arguments are supplied, standard normal variates N(0,1) are produced. The values are produced using the Ziggurat method (Marsaglia and Tsang, 2000).
See also randgen, mnormal, muniform.
Arguments: | x (series or vector) |
r (scalar) |
Returns the Net Present Value of x, considered as a sequence of payments (negative) and receipts (positive), evaluated at annual discount rate r, which must be expressed as a decimal fraction, not a percentage (0.05 rather than 5%). The first value is taken as dated "now" and is not discounted. To emulate an NPV function in which the first value is discounted, prepend zero to the input sequence.
Supported data frequencies are annual, quarterly, monthly, and undated (undated data are treated as if annual).
Arguments: | &b (reference to matrix) |
f (function call) | |
g (function call, optional) | |
h (function call, optional) |
Numerical maximization via the Newton–Raphson method. On input the vector b should hold the initial values of a set of parameters, and the argument f should specify a call to a function that calculates the (scalar) criterion to be maximized, given the current parameter values and any other relevant data. If the object is in fact minimization, this function should return the negative of the criterion. On successful completion, NRmax returns the maximized value of the criterion, and b holds the parameter values which produce the maximum.
The optional third and fourth arguments provide means of supplying analytical derivatives and an analytical (negative) Hessian, respectively. The functions referenced by g and h must take as their first argument a pre-defined matrix that is of the correct size to contain the gradient or Hessian, respectively, given in pointer form. They also must take the parameter vector as an argument (in pointer form or otherwise). Other arguments are optional. If either or both of the optional arguments are omitted, a numerical approximation is used.
For more details and examples see the chapter on numerical methods in chapter 31 of the Gretl User's Guide. See also BFGSmax, fdjac.
Argument: | A (matrix) |
Computes the right nullspace of A, via the singular value decomposition: the result is a matrix B such that the product AB is a zero matrix, except when A has full column rank, in which case an empty matrix is returned. Otherwise, if A is m x n, B will be n by (n – r), where r is the rank of A.
Returns a series of consecutive integers, setting 1 at the start of the dataset. Note that the result is invariant to subsampling. This function is especially useful with time-series datasets. Note: you can write t instead of obs with the same effect.
Argument: | t (integer) |
Returns the observation label for observation t, where t is a 1-based index. The inverse function is provided by obsnum.
Argument: | s (string) |
Returns an integer corresponding to the observation specified by the string s. Note that the result is invariant to subsampling. This function is especially useful with time-series datasets. For example, the following code
open denmark k = obsnum(1980:1)
yields k = 25, indicating that the first quarter of 1980 is the 25th observation in the denmark dataset.
Argument: | x (scalar, series, matrix or list) |
If x is a scalar, returns 1 if x is not NA, otherwise 0. If x is a series, returns a series with value 1 at observations with non-missing values and zeros elsewhere. If x is a list, the output is a series with 0 at observations for which at least one series in the list has a missing value, and 1 otherwise.
If x is a matrix the behavior is a little different, since matrices cannot contain NAs: the function returns a matrix of the same dimensions as x, with 1s in positions corresponding to finite elements of x and 0s in positions where the elements are non-finite (either infinities or not-a-number, as per the IEEE 754 standard).
See also missing, misszero, zeromiss. But note that these functions are not applicable to matrices.
Argument: | X (matrix) |
Returns the 1-norm of the matrix X, that is, the maximum across the columns of X of the sum of absolute values of the column elements.
Arguments: | r (integer) |
c (integer) |
Outputs a matrix with r rows and c columns, filled with ones.
Argument: | y (series) |
Only applicable if the currently open dataset has a panel structure. Computes the forward orthogonal deviations for variable y.
This transformation is sometimes used instead of differencing to remove individual effects from panel data. For compatibility with first differences, the deviations are stored one step ahead of their true temporal location (that is, the value at observation t is the deviation that, strictly speaking, belongs at t – 1). That way one loses the first observation in each time series, not the last.
Arguments: | d (string) |
... (see below) | |
x (scalar, series or matrix) |
Probability density function calculator. Returns the density at x of the distribution identified by the code d. See cdf for details of the required (scalar) arguments. The distributions supported by the pdf function are the normal, Student's t, chi-square, F, Gamma, Weibull, Generalized Error, Binomial and Poisson. Note that for the Binomial and the Poisson what's calculated is in fact the probability mass at the specified point. For Student's t, chi-square, F the noncentral variants are supported too.
For the normal distribution, see also dnorm.
Arguments: | x (series or vector) |
bandwidth (scalar, optional) |
If only the first argument is given, computes the sample periodogram for the given series or vector. If the second argument is given, computes an estimate of the spectrum of x using a Bartlett lag window of the given bandwidth, up to a maximum of half the number of observations (T/2).
Returns a matrix with two columns and T/2 rows: the first column holds the frequency, ω, from 2π/T to π, and the second the corresponding spectral density.
Argument: | v (vector) |
Only applicable if the currently open dataset has a panel structure. Performs the inverse operation of pshrink. That is, given a vector of length equal to the number of individuals in the current panel sample, it returns a series in which each value is repeated T times, for T the time-series length of the panel. The resulting series is therefore non-time varying.
Arguments: | y (series) |
mask (series, optional) |
Only applicable if the current dataset has a panel structure. Returns a series holding the maxima of variable y for each cross-sectional unit (repeated for each time period).
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
See also pmin, pmean, pnobs, psd, pxsum, pshrink, psum.
Arguments: | y (series) |
mask (series, optional) |
Only applicable if the currentl dataset has a panel structure. Returns a series holding the time-mean of variable y for each cross-sectional unit, the values being repeated for each period. Missing observations are skipped in calculating the means.
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
See also pmax, pmin, pnobs, psd, pxsum, pshrink, psum.
Arguments: | y (series) |
mask (series, optional) |
Only applicable if the current dataset has a panel structure. Returns a series holding the minima of variable y for each cross-sectional unit (repeated for each time period).
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
See also pmax, pmean, pnobs, psd, pshrink, psum.
Arguments: | y (series) |
mask (series, optional) |
Only applicable if the current dataset has a panel structure. Returns a series holding the number of valid observations of variable y for each cross-sectional unit (repeated for each time period).
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
See also pmax, pmin, pmean, psd, pshrink, psum.
Argument: | a (vector) |
Finds the roots of a polynomial. If the polynomial is of degree p, the vector a should contain p + 1 coefficients in ascending order, i.e. starting with the constant and ending with the coefficient on x^{p}.
If all the roots are real they are returned in a column vector of length p, otherwise a p x 2 matrix is returned, the real parts in the first column and the imaginary parts in the second.
Arguments: | y (series) |
q (integer) |
Fits a polynomial trend of order q to the input series y using the method of orthogonal polynomials. The series returned holds the fitted values.
Arguments: | X (matrix) |
p (integer) | |
covmat (boolean, optional) |
Let the matrix X be T x k, containing T observations on k variables. The argument p must be a positive integer less than or equal to k. This function returns a T x p matrix, P, holding the first p principal components of X.
The optional third argument acts as a boolean switch: if it is non-zero the principal components are computed on the basis of the covariance matrix of the columns of X (the default is to use the correlation matrix).
The elements of P are computed as the sum from i to k of Z_{ti} times v_{ji}, where Z_{ti} is the standardized value of variable i at observation t and v_{ji} is the jth eigenvector of the correlation (or covariance) matrix of the X_{i}s, with the eigenvectors ordered by decreasing value of the corresponding eigenvalues.
Argument: | X (matrix) |
Returns the product of the elements of X, by column. See also prodr, meanc, sdc, sumc.
Argument: | X (matrix) |
Returns the product of the elements of X, by row. See also prodc, meanr, sumr.
Arguments: | y (series) |
mask (series, optional) |
Only applicable if the current dataset has a panel structure. Returns a series holding the sample standard deviation of variable y for each cross-sectional unit (with the values repeated for each time period). The denominator used is the sample size for each unit minus 1, unless the number of valid observations for the given unit is 1 (in which case 0 is returned) or 0 (in which case NA is returned).
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
Note: this function makes it possible to check whether a given variable (say, X) is time-invariant via the condition max(psd(X)) == 0.
See also pmax, pmin, pmean, pnobs, pshrink, psum.
Argument: | A (symmetric matrix) |
Performs a generalized variant of the Cholesky decomposition of the matrix A, which must be positive semidefinite (but which may be singular). If the input matrix is not square an error is flagged, but symmetry is assumed and not tested; only the lower triangle of A is read. The result is a lower-triangular matrix L which satisfies A = LL'. Indeterminate elements in the solution are set to zero.
For the case where A is positive definite, see cholesky.
Argument: | y (series) |
Only applicable if the current dataset has a panel structure. Returns a column vector holding the first valid observation for the series y for each cross-sectional unit in the panel, over the current sample range. If a unit has no valid observations for the input series it is skipped.
This function provides a means of compacting the series returned by functions such as pmax and pmean, in which a value pertaining to each cross-sectional unit is repeated for each time period.
See pexpand for the inverse operation.
Arguments: | y (series) |
mask (series, optional) |
This function is applicable only if the current dataset has a panel structure. It returns a series holding the sum over time of variable y for each cross-sectional unit, the values being repeated for each period. Missing observations are skipped in calculating the sums.
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
See also pmax, pmean, pmin, pnobs, psd, pxsum, pshrink.
Arguments: | c (character) |
... (see below) | |
x (scalar, series or matrix) |
P-value calculator. Returns P(X > x), where the distribution of X is determined by the character c. Between the arguments c and x, zero or more additional arguments are required to specify the parameters of the distribution; see cdf for details. The distributions supported by the pval function are the standard normal, t, Chi square, F, gamma, binomial, Poisson, Weibull and Generalized Error.
See also critical, invcdf, urcpval, imhof.
Arguments: | y (series) |
mask (series, optional) |
Only applicable if the current dataset has a panel structure. Returns a series holding the number of valid observations of y in each time period (this count being repeated for each unit).
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
Note that this function works in a different dimension from the pnobs function.
Arguments: | y (series) |
mask (series, optional) |
Only applicable if the current dataset has a panel structure. Returns a series holding the sum of the values of y for each cross-sectional unit in each period (the values being repeated for each unit).
If the optional second argument is provided then observations for which the value of mask is zero are ignored.
Note that this function works in a different dimension from the psum function.
Arguments: | x (matrix) |
A (symmetric matrix) |
Computes the quadratic form Y = xAx'. Using this function instead of ordinary matrix multiplication guarantees more speed and better accuracy, when A is a generic symmetric matrix. However, in the special case when A is the identity matrix, the simple expression x'x performs much better than qform(x',I(rows(x)).
If x and A are not conformable, or A is not symmetric, an error is returned.
Arguments: | X2 (scalar) |
df (integer) | |
p1 (scalar) | |
p2 (scalar) |
P-values for the test statistic from the QLR sup-Wald test for a structural break at an unknown point (see qlrtest), as per Bruce Hansen (1997).
The first argument, X2, denotes the (chi-square form of) the maximum Wald test statistic and df denotes its degrees of freedom. The third and fourth arguments represent, as decimal fractions of the overall estimation range, the starting and ending points of the central range of observations over which the successive Wald tests are calculated. For example if the standard approach of 15 percent trimming is adopted, you would set p1 to 0.15 and p2 to 0.85.
Argument: | x (scalar, series or matrix) |
Returns quantiles for the standard normal distribution. If x is not between 0 and 1, NA is returned. See also cnorm, dnorm.
Arguments: | X (matrix) |
&R (reference to matrix, or null) |
Computes the QR decomposition of an m x n matrix X, that is X = QR where Q is an m x n orthogonal matrix and R is an n x n upper triangular matrix. The matrix Q is returned directly, while R can be retrieved via the optional second argument.
See also eigengen, eigensym, svd.
Arguments: | n (integer) |
type (integer, optional) | |
a (scalar, optional) | |
b (scalar, optional) |
Returns an n x 2 matrix for use with Gaussian quadrature (numerical integration). The first column holds the nodes or abscissae, the second the weights.
The first argument specifies the number of points (rows) to compute. The second argument codes for the type of quadrature: use 1 for Gauss–Hermite (the default); 2 for Gauss–Legendre; or 3 for Gauss–Laguerre. The significance of the optional parameters a and b depends on the selected type, as explained below.
Gaussian quadrature is a method of approximating numerically the definite integral of some function of interest. Let the function be represented as the product f(x)W(x). The types of quadrature differ in the specification of the component W(x): in the Hermite case this is exp(–x^{2}); in the Laguerre case, exp(–x); and in the Legendre case simply W(x) = 1.
For each specification of W, one can compute a set of nodes, x_{i}, and weights, w_{i}, such that the sum from i=1 to n of w_{i} f(x_{i}) approximates the desired integral. The method of Golub and Welsch (1969) is used.
When the Gauss–Legendre type is selected, the optional arguments a and b can be used to control the lower and upper limits of integration, the default values being –1 and 1. (In Hermite quadrature the limits are fixed at minus and plus infinity, while in the Laguerre case they are fixed at 0 and infinity.)
In the Hermite case a and b play a different role: they can be used to replace the default form of W(x) with the (closely related) normal distribution with mean a and standard deviation b. Supplying values of 0 and 1 for these parameters, for example, has the effect of making W(x) into the standard normal pdf, which is equivalent to multiplying the default nodes by the square root of two and dividing the weights by the square root of π.
Arguments: | y (series or matrix) |
p (scalar between 0 and 1) |
If y is a series, returns the p-quantile for the series. For example, when p = 0.5, the median is returned.
If y is a matrix, returns a row vector containing the p-quantiles for the columns of y; that is, each column is treated as a series.
In addition, for matrix y an alternate form of the second argument is supported: p may be given as a vector. In that case the return value is an m x n matrix, where m is the number of elements in p and n is the number of columns in y.
Arguments: | d (string) |
p1 (scalar or series) | |
p2 (scalar or series, conditional) | |
p3 (scalar, conditional) |
All-purpose random number generator. The argument d is a string (in most cases just a single character) which specifies the distribution from which the pseudo-random numbers should be drawn. The arguments p1 to p3 specify the parameters of the selected distribution; the number of such parameters depends on the distribution. For distributions other than the beta-binomial, the parameters p1 and (if applicable) p2 may be given as either scalars or series: if they are given as scalars the output series is identically distributed, while if a series is given for p1 or p2 the distribution is conditional on the parameter value at each observation. In the case of the beta-binomial all the parameters must be scalars.
Specifics are given below: the string code for each distribution is shown in parentheses, followed by the interpretation of the argument p1 and, where applicable, p2 and p3.
Uniform (continuous) (u or U): minimum, maximum
Uniform (discrete) (i): minimum, maximum
Normal (z, n, or N): mean, standard deviation
Student's t (t): degrees of freedom
Chi square (c, x, or X): degrees of freedom
Snedecor's F (f or F): df (num.), df (den.)
Gamma (g or G): shape, scale
Binomial (b or B): probability, number of trials
Poisson (p or P): mean
Weibull (w or W): shape, scale
Generalized Error (E): shape
Beta (beta): shape1, shape2
Beta-Binomial (bb): trials, shape1, shape2
See also normal, uniform, mrandgen, randgen1.
Arguments: | d (character) |
p1 (scalar) | |
p2 (scalar, conditional) |
Works like randgen except that the return value is a scalar rather than a series.
The first example above calls for a value from the standard normal distribution, while the second specifies a drawing from the Gamma distribution with shape 3 and scale 2.5.
See also mrandgen.
Arguments: | min (integer) |
max (integer) |
Returns a pseudo-random integer in the closed interval [min, max]. See also randgen.
Argument: | X (matrix) |
Returns the rank of X, numerically computed via the singular value decomposition. See also svd.
Argument: | y (series or vector) |
Returns a series or vector with the ranks of y. The rank for observation i is the number of elements that are less than y_{i} plus one half the number of elements that are equal to y_{i}. (Intuitively, you may think of chess points, where victory gives you one point and a draw gives you half a point.) One is added so the lowest rank is 1 instead of 0.
Argument: | A (square matrix) |
Returns the reciprocal condition number for A with respect to the 1-norm. In many circumstances, this is a better measure of the sensitivity of A to numerical operations such as inversion than the determinant.
The value is computed as the reciprocal of the product, 1-norm of A times 1-norm of A-inverse.
Arguments: | fname (string) |
codeset (string, optional) |
If a file by the name of fname exists and is readable, returns a string containing the content of this file, otherwise flags an error. If fname does not contain a full path specification, it will be looked for in several "likely" locations, beginning with the currently set workdir.
If fname starts with the identifier of a supported internet protocol (http://, ftp:// or https://), libcurl is invoked to download the resource. See also curl for more elaborate downloading operations.
If the text to be read is not encoded in UTF-8, gretl will try recoding it from the current locale codeset if that is not UTF-8, or from ISO-8859-15 otherwise. If this simple default does not meet your needs you can use the optional second argument to specify a codeset. For example, if you want to read text in Microsoft codepage 1251 and that is not your locale codeset, you should give a second argument of "cp1251".
Examples:
string web_page = readfile("http://gretl.sourceforge.net/") print web_page string current_settings = readfile("@dotdir/.gretl2rc") print current_settings
Also see the sscanf and getline functions.
Arguments: | s (string) |
match (string) | |
repl (string) |
Returns a copy of s in which all occurrences of the pattern match are replaced using repl. The arguments match and repl are interpreted as Perl-style regular expressions.
See also strsub for simple substitution of literal strings.
Argument: | fname (string) |
If a file by the name of fname exists and is writable by the user, removes (deletes) the named file. Returns 0 on successful completion, non-zero if there is no such file or the file cannot be removed.
If fname contains a full path specification, gretl will attempt to delete that file and return an error if the file doesn't exist or can't be deleted for some reason (such as insufficient privileges). If fname does not contain a full path, then it will be assumed that the given file name is relative to workdir. If the file doesn't exist or is unwritable, no other directories will be searched.
Arguments: | x (series or matrix) |
find (scalar or vector) | |
subst (scalar or vector) |
Replaces each element of x equal to the i-th element of find with the corresponding element of subst.
If find is a scalar, subst must also be a scalar. If find and subst are both vectors, they must have the same number of elements. But if find is a vector and subst a scalar, then all matches will be replaced by subst.
Example:
a = {1,2,3;3,4,5} find = {1,3,4} subst = {-1,-8, 0} b = replace(a, find, subst) print a b
produces
a (2 x 3) 1 2 3 3 4 5 b (2 x 3) -1 2 -8 -8 0 5
Arguments: | x (series or matrix) |
blocksize (integer, optional) |
The initial description of this function pertains to cross-sectional or time-series data; see below for the case of panel data.
Resamples from x with replacement. In the case of a series argument, each value of the returned series, y_{t}, is drawn from among all the values of x_{t} with equal probability. When a matrix argument is given, each row of the returned matrix is drawn from the rows of x with equal probability.
The optional argument blocksize represents the block size for resampling by moving blocks. If this argument is given it should be a positive integer greater than or equal to 2. The effect is that the output is composed by random selection with replacement from among all the possible contiguous sequences of length blocksize in the input. (In the case of matrix input, this means contiguous rows.) If the length of the data is not an integer multiple of the block size, the last selected block is truncated to fit.
If the argument x is a series and the dataset takes the form of a panel, resampling by moving blocks is not supported. The basic form of resampling is supported, but has this specific interpretation: the data are resampled "by individual". Suppose you have a panel in which 100 individuals are observed over 5 periods. Then the returned series will again be composed of 100 blocks of 5 observations: each block will be drawn with equal probability from the 100 individual time series, with the time-series order preserved.
Argument: | x (scalar, series or matrix) |
Rounds to the nearest integer. Note that when x lies halfway between two integers, rounding is done "away from zero", so for example 2.5 rounds to 3, but round(-3.5) gives –4. This is a common convention in spreadsheet programs, but other software may yield different results. See also ceil, floor, int.
Arguments: | M (matrix) |
S (array of strings or list) |
Attaches names to the rows of the m x n matrix M. If S is a named list, the names are taken from the names of the listed series; the list must have m members. If S is an array of strings, it should contain m elements. For backward caompatibility, a single string may also be given as the second argument; in that case it should contain m space-separated substrings.
The return value is 0 on successful completion, non-zero on error. See also colnames.
Example:
matrix M = {1, 2; 2, 1; 4, 1} strings S = array(3) S[1] = "Row1" S[2] = "Row2" S[3] = "Row3" rownames(M, S) print M
Argument: | X (matrix) |
Returns the number of rows of the matrix X. See also cols, mshape, unvech, vec, vech.
Argument: | x (series or list) |
If x is a series, returns the (scalar) sample standard deviation, skipping any missing observations.
If x is a list, returns a series y such that y_{t} is the sample standard deviation of the values of the variables in the list at observation t, or NA if there are any missing values at t.
Arguments: | X (matrix) |
df (scalar, optional) |
Returns the standard deviations of the columns of X. If df is positive it is used as the divisor for the column variances, otherwise the divisor is the number of rows in X (that is, no degrees of freedom correction is applied). See also meanc, sumc.
Argument: | y (series or list) |
Computes seasonal differences: y(t) - y(t-k), where k is the periodicity of the current dataset (see $pd). Starting values are set to NA.
When a list is returned, the individual variables are automatically named according to the template sd_varname where varname is the name of the original series. The name is truncated if necessary, and may be adjusted in case of non-uniqueness in the set of names thus constructed.
Arguments: | baseline (integer, optional) |
center (boolean, optional) |
Applicable only if the dataset has a time-series structure with periodicity greater than 1. Returns a list of dummy variables coding for the period or season, named S1, S2 and so on.
The optional baseline argument can be used to exclude one period from the set of dummies. For example, if you give a baseline value of 1 with quarterly data the returned list will hold dummies for quarters 2, 3 and 4 only. If this argument is omitted or set to zero a full set of dummies is generated; if non-zero, it must be an integer from 1 to the periodicity of the data.
The center argument, if non-zero, calls for the dummies to be centered; that is, to have their population mean subtracted. For example, with quarterly data centered seasonals will have values –0.25 and 0.75 rather than 0 and 1.
Arguments: | A (matrix) |
b (row vector) |
Selects from A only the columns for which the corresponding element of b is non-zero. b must be a row vector with the same number of columns as A.
Arguments: | A (matrix) |
b (column vector) |
Selects from A only the rows for which the corresponding element of b is non-zero. b must be a column vector with the same number of rows as A.
Arguments: | a (scalar) |
b (scalar) | |
k (scalar, optional) |
Given only two arguments, returns a row vector filled with values from a to b with an increment of 1, or a decrement of 1 if a is greater than b.
If the third argument is given, returns a row vector containing a sequence of values starting with a and incremented (or decremented, if a is greater than b) by k at each step. The final value is the largest member of the sequence that is less than or equal to b (or mutatis mutandis for a greater than b). The argument k must be positive.
Arguments: | b (bundle) |
key (string) | |
note (string) |
Sets a descriptive note for the object identified by key in the bundle b. This note will be shown when the print command is used on the bundle. This function returns 0 on success or non-zero on failure (for example, if there is no object in b under the given key).
Arguments: | &b (reference to matrix) |
f (function call) | |
maxit (integer, optional) |
Implements simulated annealing, which may be helpful in improving the initialization for a numerical optimization problem.
On input the first argument holds the initial value of a parameter vector and the second argument specifies a function call which returns the (scalar) value of the maximand. The optional third argument specifies the maximum number of iterations (which defaults to 1024). On successful completion, simann returns the final value of the maximand and b holds the associated parameter vector.
For more details and an example see the chapter on numerical methods in chapter 31 of the Gretl User's Guide. See also BFGSmax, NRmax.
Argument: | x (scalar, series or matrix) |
Returns the sine of x. See also cos, tan, atan.
Argument: | x (scalar, series or matrix) |
Returns the hyperbolic sine of x.
Argument: | x (series) |
Returns the skewness value for the series x, skipping any missing observations.
Argument: | x (series or vector) |
Sorts x in ascending order, skipping observations with missing values when x is a series. See also dsort, values. For matrices specifically, see msortby.
Arguments: | y1 (series) |
y2 (series) |
Returns a series containing the elements of y2 sorted by increasing value of the first argument, y1. See also sort, ranking.
Arguments: | format (string) |
... (see below) |
The returned string is constructed by printing the values of the trailing arguments, indicated by the dots above, under the control of format. It is meant to give you great flexibility in creating strings. The format is used to specify the precise way in which you want the arguments to be printed.
In general, format must be an expression that evaluates to a string, but in most cases will just be a string literal (an alphanumeric sequence surrounded by double quotes). Some character sequences in the format have a special meaning: those beginning with the percent character (%) are interpreted as "placeholders" for the items contained in the argument list; moreover, special characters such as the newline character are represented via a combination beginning with a backslash.
For example, the code below
scalar x = sqrt(5) string claim = sprintf("sqrt(%d) is (roughly) %6.4f.\n", 5, x) print claim
will output
sqrt(5) is (roughly) 2.2361.
where %d indicates that we want an integer at that place in the output; since it is the leftmost "percent" expression, it is matched to the first argument, that is 5. The second special sequence is %6.4f, which stands for a decimal value with 4 digits after the decimal separator and at least 6 digits wide. The number of such sequences must match the number of arguments following the format string.
See the help page for the printf command for more details about the syntax you can use in format strings.
Arguments: | L (list) |
cross-products (boolean, optional) |
Returns a list that references the squares of the variables in the list L, named on the pattern sq_varname. If the optional second argument is present and has a non-zero value, the returned list also includes the cross-products of the elements of L; these are named on the pattern var1_var2. In these patterns the input variable names are truncated if need be, and the output names may be adjusted in case of duplication of names in the returned list.
Argument: | x (scalar, series or matrix) |
Returns the positive square root of x; produces NA for negative values.
Note that if the argument is a matrix the operation is performed element by element and, since matrices cannot contain NA, negative values generate an error. For the "matrix square root" see cholesky.
Arguments: | src (string) |
format (string) | |
... (see below) |
Reads values from src under the control of format and assigns these values to one or more trailing arguments, indicated by the dots above. Returns the number of values assigned. This is a simplified version of the sscanf function in the C programming language.
src may be either a literal string, enclosed in double quotes, or the name of a predefined string variable. format is defined similarly to the format string in printf (more on this below). args should be a comma-separated list containing the names of pre-defined variables: these are the targets of conversion from src. (For those used to C: one can prefix the names of numerical variables with & but this is not required.)
Literal text in format is matched against src. Conversion specifiers start with %, and recognized conversions include %f, %g or %lf for floating-point numbers; %d for integers; %s for strings; and %m for matrices. You may insert a positive integer after the percent sign: this sets the maximum number of characters to read for the given conversion (or the maximum number of rows in the case of matrix conversion). Alternatively, you can insert a literal * after the percent to suppress the conversion (thereby skipping any characters that would otherwise have been converted for the given type). For example, %3d converts the next 3 characters in source to an integer, if possible; %*g skips as many characters in source as could be converted to a single floating-point number.
Matrix conversion works thus: the scanner reads a line of input and counts the (space- or tab-separated) number of numeric fields. This defines the number of columns in the matrix. By default, reading then proceeds for as many lines (rows) as contain the same number of numeric columns, but the maximum number of rows to read can be limited as described above.
In addition to %s conversion for strings, a simplified version of the C format %N[chars] is available. In this format N is the maximum number of characters to read and chars is a set of acceptable characters, enclosed in square brackets: reading stops if N is reached or if a character not in chars is encountered. The function of chars can be reversed by giving a circumflex, ^, as the first character; in that case reading stops if a character in the given set is found. (Unlike C, the hyphen does not play a special role in the chars set.)
If the source string does not (fully) match the format, the number of conversions may fall short of the number of arguments given. This is not in itself an error so far as gretl is concerned. However, you may wish to check the number of conversions performed; this is given by the return value.
Some examples follow:
scalar x scalar y sscanf("123456", "%3d%3d", x, y) sprintf S, "1 2 3 4\n5 6 7 8" S matrix m sscanf(S, "%m", m) print m
Argument: | y (series) |
Returns the sum of squared deviations from the mean for the non-missing observations in series y. See also var.
Arguments: | y (series) |
S (array of strings) |
Provides a means of defining string values for the series y. Two conditions must be satisfied for this to work: the target series must have nothing but integer values, none of them less than 1, and the array S must have at least n elements where n is the largest value in y. In addition each element of S must be valid UTF-8. See also strvals.
The value returned is zero on success or a positive error code on error.
Argument: | s (string) |
Returns the number of characters in the string s. Note that this does not necessarily equal the number of bytes if some characters are outside of the printable-ASCII range.
Example:
string s = "regression" scalar number = strlen(s) print number
Arguments: | s1 (string) |
s2 (string) | |
n (integer, optional) |
Compares the two string arguments and returns an integer less than, equal to, or greater than zero if s1 is found, respectively, to be less than, to match, or be greater than s2, up to the first n characters. If n is omitted the comparison proceeds as far as possible.
Note that if you just want to compare two strings for equality, that can be done without using a function, as in if (s1 == s2) ...
Arguments: | s (string) |
i (integer, optional) |
With no second argument, returns the array of strings that results from the splitting of s on white space.
If the second argument is provided, returns space-separated element i from the string s. The index i is 1-based, and it is an error if i is less than 1. In case s contains no spaces and i equals 1, a copy of the entire input string is returned; otherwise, in case i exceeds the number of space-separated elements an empty string is returned.
Examples:
string basket = "banana apple jackfruit orange" strings fruits = strsplit(basket) eval fruits[1] eval fruits[2] eval fruits[3] eval fruits[4] string favorite = strsplit(basket, 3) eval favorite
Arguments: | s1 (string) |
s2 (string) |
Searches s1 for an occurrence of the string s2. If a match is found, returns a copy of the portion of s1 that starts with s2, otherwise returns an empty string.
Example:
string s1 = "Gretl is an econometrics package" string s2 = strstr(s1, "an") print s2
Argument: | s (string) |
Returns a copy of the argument s from which leading and trailing white space have been removed.
Example:
string s1 = " A lot of white space. " string s2 = strstrip(s1) print s1 s2
Arguments: | s (string) |
find (string) | |
subst (string) |
Returns a copy of s in which all occurrences of find are replaced by subst. See also regsub for more complex string replacement via regular expressions.
Example:
string s1 = "Hello, Gretl!" string s2 = strsub(s1, "Gretl", "Hansl") print s2
Argument: | y (series) |
If the series y is string-valued, returns an array containing all its distinct values, ordered by the associated numerical values starting at 1. If y is not string-valued an empty strings array is returned. See also stringify.
Arguments: | s (string) |
start (integer) | |
end (integer) |
Returns a substring of s, from the character with (1-based) index start to that with index end, inclusive.
Examples:
string s1 = "Hello, Gretl!" string s2 = substr(s1, 8, 12) print s2 string s3 = substr("Hello, Gretl!", 8, 12) print s3
Argument: | x (series, matrix or list) |
If x is a series, returns the (scalar) sum of the non-missing observations in x. See also sumall.
If x is a matrix, returns the sum of the elements of the matrix.
If x is a list, returns a series y such that y_{t} is the sum of the values of the variables in the list at observation t, or NA if there are any missing values at t.
Argument: | x (series) |
Returns the sum of the observations of x over the current sample range, or NA if there are any missing values. Use sum is you want missing values to be skipped.
Argument: | X (matrix) |
Returns the sums of the columns of X. See also meanc, sumr.
Argument: | X (matrix) |
Returns the sums of the rows of X. See also meanr, sumc.
Arguments: | X (matrix) |
&U (reference to matrix, or null) | |
&V (reference to matrix, or null) |
Performs the singular values decomposition of the matrix X.
The singular values are returned in a row vector. The left and/or right singular vectors U and V may be obtained by supplying non-null values for arguments 2 and 3, respectively. For any matrix A, the code
s = svd(A, &U, &V) B = (U .* s) * V
should yield B identical to A (apart from machine precision).
See also eigengen, eigensym, qrdecomp.
Argument: | x (scalar, series or matrix) |
Returns the tangent of x. See also atan, cos, sin.
Argument: | x (scalar, series or matrix) |
Returns the hyperbolic tangent of x.
Arguments: | c (vector) |
r (vector) | |
b (vector) |
Solves a Toeplitz system of linear equations, that is Tx = b where T is a square matrix whose element T_{i,j} equals c_{i-j} for i>=j and r_{j-i} for i<=j. Note that the first elements of c and r must be equal, otherwise an error is returned. Upon successful completion, the function returns the vector x.
The algorithm used here takes advantage of the special structure of the matrix T, which makes it much more efficient than other unspecialized algorithms, especially for large problems. Warning: in certain cases, the function may spuriously issue a singularity error when in fact the matrix T is nonsingular; this problem, however, cannot arise when T is positive definite.
Argument: | s (string) |
Returns a copy of s in which any upper-case characters are converted to lower case.
Examples:
string s1 = "Hello, Gretl!" string s2 = tolower(s1) print s2 string s3 = tolower("Hello, Gretl!") print s3
Argument: | s (string) |
Returns a copy of s in which any lower-case characters are converted to upper case.
Examples:
string s1 = "Hello, Gretl!" string s2 = toupper(s1) print s2 string s3 = toupper("Hello, Gretl!") print s3
Argument: | A (square matrix) |
Returns the trace of the square matrix A, that is, the sum of its diagonal elements. See also diag.
Argument: | X (matrix) |
Returns the transpose of X. Note: this is rarely used; in order to get the transpose of a matrix, in most cases you can just use the prime operator: X'.
Arguments: | X (matrix) |
ttop (integer) | |
tbot (integer) |
Returns a matrix that is a copy of X with ttop rows trimmed at the top and tbot rows trimmed at the bottom. The latter two arguments must be non-negative, and must sum to less than the total rows of X.
Argument: | typecode (integer) |
Returns the name of the gretl data-type corresponding to typecode. This may be used in conjunction with the function inbundle. The value returned is one of "scalar", "series", "matrix", "string", "bundle", "array" or "null".
Arguments: | a (scalar) |
b (scalar) |
Generates a series of uniform pseudo-random variates in the interval (a, b), or, if no arguments are supplied, in the interval (0,1). The algorithm used by default is the SIMD-oriented Fast Mersenne Twister developed by Saito and Matsumoto (2008).
See also randgen, normal, mnormal, muniform.
Argument: | x (series or vector) |
Returns a vector containing the distinct elements of x, not sorted but in their order of appearance. See values for a variant that sorts the elements.
Argument: | v (vector) |
Returns an n x n symmetric matrix obtained by rearranging the elements of v. The number of elements in v must be a triangular integer — i.e., a number k such that an integer n exists with the property k = n(n+1)/2. This is the inverse of the function vech.
Argument: | A (square matrix) |
Returns an n x n upper triangular matrix: the elements on and above the diagonal are equal to the corresponding elements of A; the remaining elements are zero.
Arguments: | tau (scalar) |
n (integer) | |
niv (integer) | |
itv (integer) |
P-values for the test statistic from the Dickey–Fuller unit-root test and the Engle–Granger cointegration test, as per James MacKinnon (1996).
The arguments are as follows: tau denotes the test statistic; n is the number of observations (or 0 for an asymptotic result); niv is the number of potentially cointegrated variables when testing for cointegration (or 1 for a univariate unit-root test); and itv is a code for the model specification: 1 for no constant, 2 for constant included, 3 for constant and linear trend, 4 for constant and quadratic trend.
Note that if the test regression is "augmented" with lags of the dependent variable, then you should give an n value of 0 to get an asymptotic result.
Argument: | x (series or vector) |
Returns a vector containing the distinct elements of x sorted in ascending order. If you wish to truncate the values to integers before applying this function, use the expression values(int(x)).
Argument: | x (series or list) |
If x is a series, returns the (scalar) sample variance, skipping any missing observations.
If x is a list, returns a series y such that y_{t} is the sample variance of the values of the variables in the list at observation t, or NA if there are any missing values at t.
In each case the sum of squared deviations from the mean is divided by (n – 1) for n > 1. Otherwise the variance is given as zero if n = 1, or as NA if n = 0.
Argument: | v (integer or list) |
If given an integer argument, returns the name of the variable with ID number v, or generates an error if there is no such variable.
If given a list argument, returns a string containing the names of the variables in the list, separated by commas. If the supplied list is empty, so is the returned string. To get an array of strings as return value, use varnames instead.
Example:
open broiler.gdt string s = varname(7) print s
Argument: | L (list) |
Returns an array of strings containing the names of the variables in the list L. If the supplied list is empty, so is the returned array.
Example:
open keane.gdt list L = year wage status strings S = varnames(L) eval S[1] eval S[2] eval S[3]
Argument: | varname (string) |
Returns the ID number of the variable called varname, or NA is there is no such variable.
Arguments: | A (matrix) |
U (matrix) | |
y0 (matrix) |
Simulates a p-order n-variable VAR, that is y(t) = A1 y(t-1) + ... + Ap y(t-p) + u(t). The coefficient matrix A is composed by stacking the A_{i} matrices horizontally; it is n x np, with one row per equation. This corresponds to the first n rows of the matrix $compan provided by gretl's var and vecm commands.
The u_t vectors are contained (as rows) in U (T x n). Initial values are in y0 (p x n).
If the VAR contains deterministic terms and/or exogenous regressors, these can be handled by folding them into the U matrix: each row of U then becomes u(t) = B'x(t) + e(t).
The output matrix has T + p rows and n columns; it holds the initial p values of the endogenous variables plus T simulated values.
Argument: | X (matrix) |
Stacks the columns of X as a column vector. See also mshape, unvech, vech.
Argument: | A (square matrix) |
Returns in a column vector the elements of A on and above the diagonal. Typically, this function is used on symmetric matrices; in this case, it can be undone by the function unvech. See also vec.
Arguments: | year (scalar or series) |
month (scalar or series) | |
day (scalar or series) |
Returns the day of the week (Sunday = 0, Monday = 1, etc.) for the date(s) specified by the three arguments, or NA if the date is invalid. Note that all three arguments must be of the same type, either scalars (integers) or series.
Arguments: | Y (list) |
W (list) |
Returns a series y such that y_{t} is the weighted mean of the values of the variables in list Y at observation t, the respective weights given by the values of the variables in list W at t. The weights can therefore be time-varying. The lists Y and W must be of the same length and the weights must be non-negative.
Arguments: | Y (list) |
W (list) |
Returns a series y such that y_{t} is the weighted sample standard deviation of the values of the variables in list Y at observation t, the respective weights given by the values of the variables in list W at t. The weights can therefore be time-varying. The lists Y and W must be of the same length and the weights must be non-negative.
Arguments: | X (list) |
W (list) |
Returns a series y such that y_{t} is the weighted sample variance of the values of the variables in list X at observation t, the respective weights given by the values of the variables in list W at t. The weights can therefore be time-varying. The lists Y and W must be of the same length and the weights must be non-negative.
Arguments: | x (scalar) |
y (scalar) |
Returns the greater of x and y, or NA if either value is missing.
Arguments: | x (scalar) |
y (scalar) |
Returns the lesser of x and y, or NA if either value is missing.
Argument: | x (scalar or series) |
Converts zeros to NAs. If x is a series, the conversion is done element by element. See also missing, misszero, ok.
Arguments: | r (integer) |
c (integer) |
Outputs a zero matrix with r rows and c columns. See also ones, seq.