Gretl Function Reference

See also the Gretl Command Reference

The following accessors and functions are documented below.

$ahat $aic $bic $chisq $coeff $command $compan $datatype
$depvar $df $dwpval $ec $error $ess $evals $fcast
$fcerr $fevd $Fstat $gmmcrit $h $hausman $hqc $huge
$jalpha $jbeta $jvbeta $llt $lnl $macheps $mnlprobs $ncoeff
$nobs $nvars $obsdate $obsmajor $obsmicro $obsminor $pd $pi
$pvalue $rho $rsq $sample $sargan $sigma $stderr $stopwatch
$sysA $sysB $sysGamma $T $t1 $t2 $test $trsq
$uhat $unit $vcv $vecGamma $version $vma $windows $xlist
$xtxinv $yhat $ylist
abs acos acosh aggregate argname asin asinh atan
atanh atof bessel BFGSmax bkfilt boxcox bwfilt cdemean
cdf cdiv ceil cholesky chowlin cmult cnorm colname
colnames cols corr corrgm cos cosh cov critical
cum deseas det diag diagcat diff digamma dnorm
dsort dummify eigengen eigensym eigsolve epochday errmsg exp
fcstats fdjac fft ffti filter firstobs fixname floor
fracdiff gammafun getenv getline ghk gini ginv halton
hdprod hpfilt I imaxc imaxr imhof iminc iminr
inbundle infnorm inlist int inv invcdf invmills invpd
irf irr isconst isnan isnull isoconv isodate iwishart
kdensity kfilter ksimul ksmooth kurtosis lags lastobs ldet
ldiff lincomb ljungbox lngamma log log10 log2 loess
logistic lower lrvar max maxc maxr mcorr mcov
mcovg mean meanc meanr median mexp min minc
minr missing misszero mlag mnormal mols monthlen movavg
mpols mrandgen mread mreverse mrls mshape msortby muniform
mwrite mxtab nadarwat nelem ngetenv nobs normal npv
NRmax nullspace obs obslabel obsnum ok onenorm ones
orthdev pdf pergm pmax pmean pmin pnobs polroots
polyfit princomp prodc prodr psd psdroot pshrink psum
pvalue pxsum qform qnorm qrdecomp quadtable quantile randgen
randgen1 randint rank ranking rcond readfile regsub remove
replace resample round rownames rows sd sdc sdiff
selifc selifr seq setnote simann sin sinh skewness
sort sortby sqrt sscanf sst strlen strncmp strsplit
strstr strstrip strsub sum sumall sumc sumr svd
tan tanh toepsolv tolower toupper tr transp trimr
typestr uniform uniq unvech upper urcpval values var
varname varnum varsimul vec vech weekday wmean wsd
wvar xmax xmin xpx zeromiss zeros

Accessors

$ahat

Output: series

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).


$aic

Output: scalar

Returns the Akaike Information Criterion for the last estimated model, if available. See the Gretl User's Guide for details of the calculation.


$bic

Output: scalar

Returns Schwarz's Bayesian Information Criterion for the last estimated model, if available. See the Gretl User's Guide for details of the calculation.


$chisq

Output: scalar

Returns the overall chi-square statistic from the last estimated model, if available.


$coeff

Output: matrix or scalar
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.


$command

Output: string

Must follow the estimation of a model; returns the command word, for example ols or probit.


$compan

Output: matrix

Must follow the estimation of a VAR or a VECM; returns the companion matrix.


$datatype

Output: scalar

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.


$depvar

Output: string

Must follow the estimation of a single-equation model; returns the name of the dependent variable.


$df

Output: scalar

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).


$dwpval

Output: scalar

Returns the p-value for the Durbin–Watson statistic for the model last estimated, if available. This is computed using the Imhof procedure.


$ec

Output: matrix

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.


$error

Output: scalar

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

See also catch, errmsg.


$ess

Output: scalar

Returns the error sum of squares of the last estimated model, if available.


$evals

Output: matrix

Must follow the estimation of a VECM; returns a vector containing the eigenvalues that are used in computing the trace test for cointegration.


$fcast

Output: matrix

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.


$fcerr

Output: matrix

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.


$fevd

Output: matrix

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 p2 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.


$Fstat

Output: scalar

Returns the overall F-statistic from the last estimated model, if available.


$gmmcrit

Output: scalar

Must follow a gmm block. Returns the value of the GMM objective function at its minimum.


$h

Output: series

Must follow a garch command. Returns the estimated conditional variance series.


$hausman

Output: row vector

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.


$hqc

Output: scalar

Returns the Hannan-Quinn Information Criterion for the last estimated model, if available. See the Gretl User's Guide for details of the calculation.


$huge

Output: scalar

Returns a very large positive number. By default this is 1.0E100, but the value can be changed using the set command.


$jalpha

Output: matrix

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.


$jbeta

Output: matrix

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.


$jvbeta

Output: square matrix

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 

$llt

Output: series

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.


$lnl

Output: scalar

Returns the log-likelihood for the last estimated model (where applicable).


$macheps

Output: scalar

Returns the value of "machine epsilon", which gives an upper bound on the relative error due to rounding in double-precision floating point arithmetic.


$mnlprobs

Output: matrix

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.


$ncoeff

Output: integer

Returns the total number of coefficients estimated in the last model.


$nobs

Output: integer

Returns the number of observations in the currently selected sample.


$nvars

Output: integer

Returns the number of variables in the dataset (including the constant).


$obsdate

Output: series

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.


$obsmajor

Output: series

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.


$obsmicro

Output: series

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.


$obsminor

Output: series

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).

See also $obsmajor, $obsmicro.


$pd

Output: integer

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.


$pi

Output: scalar

Returns the value of π in double precision.


$pvalue

Output: scalar or matrix

Returns the p-value of the test statistic that was generated by the last explicit hypothesis-testing command, if any (e.g. chow). See 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.


$rho

Output: scalar
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).


$rsq

Output: scalar

Returns the unadjusted R2 from the last estimated model, if available.


$sample

Output: series

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

$sargan

Output: row vector

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.


$sigma

Output: scalar or matrix

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.


$stderr

Output: matrix or scalar
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.

See also $coeff, $vcv.


$stopwatch

Output: scalar

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.


$sysA

Output: matrix

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.


$sysB

Output: matrix

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.


$sysGamma

Output: matrix

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.


$T

Output: integer

Returns the number of observations used in estimating the last model.


$t1

Output: integer

Returns the 1-based index of the first observation in the currently selected sample.


$t2

Output: integer

Returns the 1-based index of the last observation in the currently selected sample.


$test

Output: scalar or matrix

Returns the value of the test statistic that was generated by the last explicit hypothesis-testing command, if any (e.g. chow). See 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.


$trsq

Output: scalar

Returns TR2 (sample size times R-squared) from the last model, if available.


$uhat

Output: series

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.


$unit

Output: series

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.


$vcv

Output: matrix or scalar
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.


$vecGamma

Output: matrix

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.


$version

Output: scalar

Returns an integer value that codes for the program version. The gretl version string takes the form x.y.z (for example, 1.7.6). The return value from this accessor is formed as 10000*x + 100*y + z, so that 1.7.6 translates as 10706.


$vma

Output: matrix

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 the Gretl User's Guide for details.


$windows

Output: integer

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.


$xlist

Output: list

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.


$xtxinv

Output: matrix

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.


$yhat

Output: series

Returns the fitted values from the last regression.


$ylist

Output: list

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.

Functions proper

abs

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the absolute value of x.


acos

Output: same type as input
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.


acosh

Output: same type as input
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.


aggregate

Output: matrix
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])

argname

Output: string
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.


asin

Output: same type as input
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.


asinh

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the inverse hyperbolic sine of x. See also sinh.


atan

Output: same type as input
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.


atanh

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the inverse hyperbolic tangent of x. See also tanh.


atof

Output: scalar
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.


bessel

Output: same type as input
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.


BFGSmax

Output: scalar
Arguments:b (vector)
f (function call)
g (function call, optional)

Numerical maximization via the method of Broyden, Fletcher, Goldfarb and Shanno. 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 the Gretl User's Guide. See also NRmax, fdjac, simann.


bkfilt

Output: series
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 following default values are used: f1 = 8, f1 = 32, k = 8. See also bwfilt, hpfilt.


boxcox

Output: series
Arguments:y (series)
d (scalar)

Returns the Box–Cox transformation with parameter d for the positive series y.

The transformed series is (yd - 1)/d for d not equal to zero, or log(y) for d = 0.


bwfilt

Output: series
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 the Gretl User's Guide for details. See also bkfilt, hpfilt.


cdemean

Output: matrix
Argument: X (matrix)

Centers the columns of matrix X around their means.


cdf

Output: same type as input
Arguments:c (character)
... (see below)
x (scalar, series or matrix)
Examples: p1 = cdf(N, -2.5) p2 = cdf(X, 3, 5.67) p3 = cdf(D, 0.25, -1, 1)

Cumulative distribution function calculator. Returns P(X <= x), where the distribution X is determined by the character c. Between the arguments c and x, zero or more additional scalar arguments are required to specify the parameters of the distribution, as follows.

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.


cdiv

Output: matrix
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.


ceil

Output: same type as input
Argument: x (scalar, series or matrix)

Ceiling function: returns the smallest integer greater than or equal to x. See also floor, int.


cholesky

Output: square matrix
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.


chowlin

Output: matrix
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.


cmult

Output: matrix
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.


cnorm

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the cumulative distribution function for a standard normal. See also dnorm, qnorm.


colname

Output: string
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.


colnames

Output: scalar
Arguments:M (matrix)
s (named list or string)

Attaches names to the columns of the T x k matrix M. If s is a named list, the column names are copied from the names of the variables; the list must have k members. If s is a string, it should contain k space-separated sub-strings. The return value is 0 on successful completion, non-zero on error. See also rownames.

Example:

	  matrix M = {1, 2; 2, 1; 4, 1}
	  colnames(M, "Col1 Col2")
	  print M

cols

Output: integer
Argument: X (matrix)

Returns the number of columns of X. See also mshape, rows, unvech, vec, vech.


corr

Output: scalar
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.


corrgm

Output: matrix
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.


cos

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the cosine of x.


cosh

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the hyperbolic cosine of x.

See also acosh, sinh, tanh.


cov

Output: scalar
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.


critical

Output: same type as input
Arguments:c (character)
... (see below)
p (scalar, series or matrix)
Examples: c1 = critical(t, 20, 0.025) c2 = critical(F, 4, 48, 0.05)

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.

See also cdf, invcdf, pvalue.


cum

Output: same type as input
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.

See also diff.


deseas

Output: series
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.


det

Output: scalar
Argument: A (square matrix)

Returns the determinant of A, computed via the LU factorization. See also ldet, rcond.


diag

Output: matrix
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.


diagcat

Output: matrix
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.


diff

Output: same type as input
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.

See also cum, ldiff, sdiff.


digamma

Output: same type as input
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.


dnorm

Output: same type as input
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)

See also cnorm, qnorm.


dsort

Output: same type as input
Argument: x (series or vector)

Sorts x in descending order, skipping observations with missing values when x is a series. See also sort, values.


dummify

Output: list
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.


eigengen

Output: matrix
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 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:

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.


eigensym

Output: matrix
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). The eigenvalues are returned in ascending order.


eigsolve

Output: matrix
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.


epochday

Output: scalar or series
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.


errmsg

Output: string
Argument: errno (integer)

Retrieves the gretl error message associated with errno. See also $error.


exp

Output: same type as input
Argument: x (scalar, series or matrix)

Returns ex. Note that in case of matrices the function acts element by element. For the matrix exponential function, see mexp.


fcstats

Output: matrix
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 the Gretl User's Guide.


fdjac

Output: matrix
Arguments:b (column vector)
fcall (function call)

Calculates the (forward-difference 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))

For more details and examples see the chapter on numerical methods in the Gretl User's Guide.

See also BFGSmax.


fft

Output: matrix
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.


ffti

Output: matrix
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.


filter

Output: series
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

yt = a0 xt + a1 xt-1 + ... aq xt-q + b1 yt-1 + ... bp yt-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 a0 and implies q=0; if it is a vector of q+1 elements, they contain the coefficients from a0 to aq. If a is null or omitted, this is equivalent to setting a0=1 and q=0.

If b is a scalar, this is used as b1 and implies p=1; if it is a vector of p elements, they contain the coefficients from b1 to bp. 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 

firstobs

Output: integer
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.


fixname

Output: string
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 last character transcribed is an underscore in which case space is skipped.


floor

Output: same type as input
Argument: y (scalar, series or matrix)

Floor function: 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.


fracdiff

Output: series
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 yt are assumed to be zero.


gammafun

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the gamma function of x.


getenv

Output: string
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.


getline

Output: scalar
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)
	  getline(s, null)

Note that although the reading position advances at each call to getline, source is not modified by this function, only target.


ghk

Output: matrix
Arguments:C (matrix)
A (matrix)
B (matrix)
U (matrix)

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 the 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.

In the following example, 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 = muniform(2, 100)

	  series Q = ghk(C, {inf1, inf2}, {sup1, sup2}, U)

gini

Output: scalar
Argument: y (series)

Returns Gini's inequality index for the series y.


ginv

Output: matrix
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.

See also inv, svd.


halton

Output: matrix
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).


hdprod

Output: matrix
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.

As far as we know, there isn't an established name for this operation in matrix algebra. "Horizontal direct product" is the way this operation is called in the GAUSS programming language.

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 

hpfilt

Output: series
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.


I

Output: square matrix
Argument: n (integer)

Returns an identity matrix with n rows and columns.


imaxc

Output: row vector
Argument: X (matrix)

Returns the row indices of the maxima of the columns of X.

See also imaxr, iminc, maxc.


imaxr

Output: column vector
Argument: X (matrix)

Returns the column indices of the maxima of the rows of X.

See also imaxc, iminr, maxr.


imhof

Output: scalar
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.


iminc

Output: row vector
Argument: X (matrix)

Returns the row indices of the minima of the columns of X.

See also iminr, imaxc, minc.


iminr

Output: column vector
Argument: X (matrix)

Returns the column indices of the mimima of the rows of X.

See also iminc, imaxr, minr.


inbundle

Output: integer
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 and 5 for bundle. The function typestr may be used to get the string corresponding to this code.


infnorm

Output: scalar
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.

See also onenorm.


inlist

Output: integer
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.


int

Output: same type as input
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.


inv

Output: matrix
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.

See also ginv, invpd.


invcdf

Output: same type as input
Arguments:c (character)
... (see below)
p (scalar, series or matrix)

Inverse cumulative distribution function 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.

See also cdf, critical, pvalue.


invmills

Output: same type as input
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.

See also cdf, cnorm, dnorm.


invpd

Output: square matrix
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.


irf

Output: matrix
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.


irr

Output: scalar
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.


isconst

Output: integer
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.


isnan

Output: same type as input
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.


isnull

Output: integer
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.


isoconv

Output: scalar
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.


isodate

Output: see below
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.


iwishart

Output: matrix
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.


kdensity

Output: matrix
Arguments:x (series)
scale (scalar, optional)
control (boolean, optional)

Computes a kernel density estimate for the series 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

kfilter

Output: scalar
Arguments:&E (reference to matrix, or null)
&V (reference to matrix, or null)
&S (reference to matrix, or null)
&P (reference to matrix, or null)
&G (reference to matrix, or null)

Requires that a Kalman filter be set up. Performs a forward, filtering pass and returns 0 on successful completion or 1 if numerical problems are encountered.

The optional matrix arguments can be used to retrieve the following information: E gets the matrix of one-step ahead prediction errors and V gets the variance matrix for these errors; S gets the matrix of estimated values of the state vector and P the variance matrix of these estimates; G gets the Kalman gain. All of these matrices have T rows, corresponding to T observations. For the column dimensions and further details see the Gretl User's Guide.

See also kalman, ksmooth, ksimul.


ksimul

Output: matrix
Arguments:v (matrix)
w (matrix)
&S (reference to matrix, or null)

Requires that a Kalman filter be set up. Performs a simulation and returns a matrix holding simulated values of the observable variables.

The argument v supplies artificial disturbances for the state transition equation and w supplies disturbances for the observation equation, if applicable. The optional argument S may be used to retrieve the simulated state vector. For details see the Gretl User's Guide.

See also kalman, kfilter, ksmooth.


ksmooth

Output: matrix
Argument: &P (reference to matrix, or null)

Requires that a Kalman filter be set up. Performs a backward, smoothing pass and returns a matrix holding smoothed estimates of the state vector. The optional argument P may be used to retrieve the MSE of the smoothed state. For details see the Gretl User's Guide.

See also kalman, kfilter, ksimul.


kurtosis

Output: scalar
Argument: x (series)

Returns the excess kurtosis of the series x, skipping any missing observations.


lags

Output: list
Arguments:p (integer)
y (series or list)
bylag (boolean, optional)

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.

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.


lastobs

Output: integer
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.


ldet

Output: scalar
Argument: A (square matrix)

Returns the natural log of the determinant of A, computed via the LU factorization. See also det, rcond.


ldiff

Output: same type as input
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.

See also diff, sdiff.


lincomb

Output: series
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.

See also wmean.


ljungbox

Output: scalar
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.


lngamma

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the log of the gamma function of x.


log

Output: same type as input
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.


log10

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the base-10 logarithm of x; produces NA for non-positive values.


log2

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the base-2 logarithm of x; produces NA for non-positive values.


loess

Output: series
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 the Gretl User's Guide for details on nonparametric methods.


logistic

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the logistic function of the argument x, that is, ex/(1 + ex). If x is a matrix, the function is applied element by element.


lower

Output: square matrix
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.

See also upper.


lrvar

Output: scalar
Arguments:y (series or vector)
k (integer)

Returns the long-run variance of y, calculated using a Bartlett kernel with window size k. If k is negative, int(T^(1/3)) is used.


max

Output: scalar or series
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.

See also min, xmax, xmin.


maxc

Output: row vector
Argument: X (matrix)

Returns a row vector containing the maxima of the columns of X.

See also imaxc, maxr, minc.


maxr

Output: column vector
Argument: X (matrix)

Returns a column vector containing the maxima of the rows of X.

See also imaxc, maxc, minr.


mcorr

Output: matrix
Argument: X (matrix)

Computes a correlation matrix treating each column of X as a variable. See also corr, cov, mcov.


mcov

Output: matrix
Argument: X (matrix)

Computes a covariance matrix treating each column of X as a variable. See also corr, cov, mcorr.


mcovg

Output: matrix
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.


mean

Output: scalar or series
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 yt 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.


meanc

Output: row vector
Argument: X (matrix)

Returns the means of the columns of X. See also meanr, sumc, sdc.


meanr

Output: column vector
Argument: X (matrix)

Returns the means of the rows of X. See also meanc, sumr.


median

Output: scalar
Argument: y (series)

The median of the non-missing observations in series y. See also quantile.


mexp

Output: square matrix
Argument: A (square matrix)

Computes the matrix exponential of A, using algorithm 11.3.1 from Golub and Van Loan (1996).


min

Output: scalar or series
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.

See also max, xmax, xmin.


minc

Output: row vector
Argument: X (matrix)

Returns the minima of the columns of X.

See also iminc, maxc, minr.


minr

Output: column vector
Argument: X (matrix)

Returns the minima of the rows of X.

See also iminr, maxr, minc.


missing

Output: same type as input
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.


misszero

Output: same type as input
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.


mlag

Output: matrix
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.


mnormal

Output: matrix
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.


mols

Output: matrix
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.

See also mpols, mrls.


monthlen

Output: integer
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).


movavg

Output: series
Arguments:x (series)
p (scalar)
control (integer, 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(t) to x(t-p+1). If a non-zero value is supplied for the optional control parameter the MA is centered, otherwise it is "trailing".

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 valid 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.


mpols

Output: matrix
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.


mrandgen

Output: matrix
Arguments:d (string)
p1 (scalar)
p2 (scalar, conditional)
p3 (scalar, conditional)
rows (integer)
cols (integer)
Examples: matrix mx = mrandgen(u, 0, 100, 50, 1) matrix mt14 = mrandgen(t, 14, 20, 20)

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.

See also mnormal, muniform.


mread

Output: matrix
Arguments:fname (string)
import (boolean, optional)

Reads a matrix from a text file. The string fname must contain the name of the file from which the matrix 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 may start with any number of comment lines, defined as lines that start with the hash mark, #; such lines are ignored. Beyond that, the content must conform to the following rules:

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.

Should an error occur (such as the file being badly formatted or inaccessible), an empty matrix is returned.

See also mwrite.


mreverse

Output: matrix
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')'

mrls

Output: matrix
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 k * n 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.


mshape

Output: matrix
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.


msortby

Output: matrix
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.


muniform

Output: matrix
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.

See also mnormal, uniform.


mwrite

Output: integer
Arguments:X (matrix)
fname (string)
export (boolean, optional)

Writes the matrix X to a plain text file named fname. The file will contain on the first line two integers, separated by a tab character, with the number of rows and columns; on the next lines, the matrix elements in scientific notation, separated by tabs (one line per row).

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.

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 command can be easily read by other programs; see the Gretl User's Guide for details.

An extension to the basic behavior of this function is available: if fname has the suffix ".gz" then the file is written with gzip compression.

See also mread.


mxtab

Output: matrix
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.

See also values.


nadarwat

Output: series
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(yi|xi) for each nonmissing element of the series x.

The kernel function K is given by K = exp(-x2 / 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 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(xi). 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.


nelem

Output: integer
Argument: L (list)

Returns the number of members in the list L.


ngetenv

Output: scalar
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.


nobs

Output: integer
Argument: y (series)

Returns the number of non-missing observations for the variable y in the currently selected sample.


normal

Output: series
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.


npv

Output: scalar
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. 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).

See also irr.


NRmax

Output: scalar
Arguments:b (vector)
f (function call)
g (function call, optional)
h (function call, optional)

Numerical maximization via the Newton–Raphson method. 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 the Gretl User's Guide. See also BFGSmax, fdjac.


nullspace

Output: matrix
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 (nr), where r is the rank of A.

See also rank, svd.


obs

Output: series

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.

See also obsnum.


obslabel

Output: string
Argument: t (integer)

Returns the observation label for observation t, where t is a 1-based index. The inverse function is provided by obsnum.


obsnum

Output: integer
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.

See also obs, obslabel.


ok

Output: see below
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.


onenorm

Output: scalar
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.

See also infnorm, rcond.


ones

Output: matrix
Arguments:r (integer)
c (integer)

Outputs a matrix with r rows and c columns, filled with ones.

See also seq, zeros.


orthdev

Output: series
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.

See also diff.


pdf

Output: same type as input
Arguments:c (character)
... (see below)
x (scalar, series or matrix)
Examples: f1 = pdf(N, -2.5) f2 = pdf(X, 3, y) f3 = pdf(W, shape, scale, y)

Probability density function calculator. Returns the density at x of the distribution identified by the code c. 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 the normal distribution, see also dnorm.


pergm

Output: matrix
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.


pmax

Output: series
Arguments:y (series)
mask (series, optional)

Only applicable if the currently open 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.


pmean

Output: series
Arguments:y (series)
mask (series, optional)

Only applicable if the currently open 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.


pmin

Output: series
Arguments:y (series)
mask (series, optional)

Only applicable if the currently open 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.


pnobs

Output: series
Arguments:y (series)
mask (series, optional)

Only applicable if the currently open 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.


polroots

Output: matrix
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 xp.

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.


polyfit

Output: series
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.


princomp

Output: matrix
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 Zti times vji, where Zti is the standardized value of variable i at observation t and vji is the jth eigenvector of the correlation (or covariance) matrix of the Xis, with the eigenvectors ordered by decreasing value of the corresponding eigenvalues.

See also eigensym.


prodc

Output: row vector
Argument: X (matrix)

Returns the product of the elements of X, by column. See also prodr, meanc, sdc, sumc.


prodr

Output: column vector
Argument: X (matrix)

Returns the product of the elements of X, by row. See also prodc, meanr, sumr.


psd

Output: series
Arguments:y (series)
mask (series, optional)

Only applicable if the currently open 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.


psdroot

Output: square matrix
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.


pshrink

Output: matrix
Argument: y (series)

Only applicable if the currently open 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.


psum

Output: series
Arguments:y (series)
mask (series, optional)

Only applicable if the currently open dataset has a panel structure. 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.


pvalue

Output: same type as input
Arguments:c (character)
... (see below)
x (scalar, series or matrix)
Examples: p1 = pvalue(z, 2.2) p2 = pvalue(X, 3, 5.67) p2 = pvalue(F, 3, 30, 5.67)

P-value calculator. Returns P(X > x), where the distribution 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.


pxsum

Output: series
Arguments:y (series)
mask (series, optional)

Only applicable if the currently open 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 pmean function.


qform

Output: matrix
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. If x and A are not conformable, or A is not symmetric, an error is returned.


qnorm

Output: same type as input
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.


qrdecomp

Output: matrix
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.


quadtable

Output: matrix
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(–x2); 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, xi, and weights, wi, such that the sum from i=1 to n of wif(xi) 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.


quantile

Output: scalar or matrix
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.


randgen

Output: series
Arguments:d (string)
p1 (scalar or series)
p2 (scalar or series, conditional)
p3 (scalar, conditional)
Examples: series x = randgen(u, 0, 100) series t14 = randgen(t, 14) series y = randgen(B, 0.6, 30) series g = randgen(G, 1, 1) series P = randgen(P, mu)

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.

See also normal, uniform, mrandgen, randgen1.


randgen1

Output: scalar
Arguments:d (character)
p1 (scalar)
p2 (scalar, conditional)
Examples: scalar x = randgen1(z, 0, 1) scalar g = randgen1(g, 3, 2.5)

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.


randint

Output: integer
Arguments:min (integer)
max (integer)

Returns a pseudo-random integer in the closed interval [min, max]. See also randgen.


rank

Output: integer
Argument: X (matrix)

Returns the rank of X, numerically computed via the singular value decomposition. See also svd.


ranking

Output: same type as input
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 yi plus one half the number of elements that are equal to yi. (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.

See also sort, sortby.


rcond

Output: scalar
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.

See also det, ldet, onenorm.


readfile

Output: string
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.

In the case where fname starts with the indentifier of a supported internet protocol (http://, ftp://, https://), libcurl is invoked to download the resource.

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".

Also see the sscanf and getline functions.


regsub

Output: string
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.


remove

Output: integer
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.


replace

Output: same type as input
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 

resample

Output: same type as input
Arguments:x (series or matrix)
b (integer, optional)

Resamples from x with replacement. In the case of a series argument, each value of the returned series, yt, is drawn from among all the values of xt 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 b represents the block length 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 b 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 length, the last selected block is truncated to fit.


round

Output: same type as input
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.


rownames

Output: integer
Arguments:M (matrix)
s (named list or string)

Attaches names to the rows of the m x n matrix M. If s is a named list, the row names are copied from the names of the variables; the list must have m members. If s is a string, it should contain m space-separated sub-strings. The return value is 0 on successful completion, non-zero on error. See also colnames.

Example:

      matrix M = {1,2;2,1;4,1} 
      rownames(M, "Row1 Row2 Row3")
      print M      

rows

Output: integer
Argument: X (matrix)

Returns the number of rows of the matrix X. See also cols, mshape, unvech, vec, vech.


sd

Output: scalar or series
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 yt 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.

See also var.


sdc

Output: row vector
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.


sdiff

Output: same type as input
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.

See also diff, ldiff.


selifc

Output: matrix
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.

See also selifr.


selifr

Output: matrix
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.

See also selifc, trimr.


seq

Output: row vector
Arguments:a (integer)
b (integer)
k (integer, optional)

Given only two arguments, returns a row vector filled with consecutive integers, with a as first element and b last. If a is greater than b the sequence will be decreasing. If either argument is not integral its fractional part is discarded.

If the third argument is given, returns a row vector containing a sequence of integers 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; if it is not integral its fractional part is discarded.

See also ones, zeros.


setnote

Output: integer
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).


simann

Output: scalar
Arguments:b (vector)
f (function call)
maxit (integer, optional)

Implements simulated annealing, which may be helpful in improving the initialization for a numerical optimization problem.

The first argument holds the intial 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.

For more details and an example see the chapter on numerical methods in the Gretl User's Guide. See also BFGSmax, NRmax.


sin

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the sine of x. See also cos, tan, atan.


sinh

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the hyperbolic sine of x.

See also asinh, cosh, tanh.


skewness

Output: scalar
Argument: x (series)

Returns the skewness value for the series x, skipping any missing observations.


sort

Output: same type as input
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.


sortby

Output: series
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.


sqrt

Output: same type as input
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.


sscanf

Output: integer
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 simplifed 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

sst

Output: scalar
Argument: y (series)

Returns the sum of squared deviations from the mean for the non-missing observations in series y. See also var.


strlen

Output: integer
Argument: s (string)

Returns the number of characters in s.


strncmp

Output: integer
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) ...


strsplit

Output: string
Arguments:s (string)
i (integer)

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.


strstr

Output: string
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.


strstrip

Output: string
Argument: s (string)

Returns a copy of the argument s from which leading and trailing white space have been removed.


strsub

Output: string
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.


sum

Output: scalar or series
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 yt 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.


sumall

Output: scalar
Argument: x (series)

Returns the sum of the observations of x over the current sample range, or NA if there are any missing values.


sumc

Output: row vector
Argument: X (matrix)

Returns the sums of the columns of X. See also meanc, sumr.


sumr

Output: column vector
Argument: X (matrix)

Returns the sums of the rows of X. See also meanr, sumc.


svd

Output: row vector
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.


tan

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the tangent of x.


tanh

Output: same type as input
Argument: x (scalar, series or matrix)

Returns the hyperbolic tangent of x.

See also atanh, cosh, sinh.


toepsolv

Output: column vector
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 Ti,j equals ci-j for i>=j and rj-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.


tolower

Output: string
Argument: s (string)

Returns a copy of s in which any upper-case characters are converted to lower case.


toupper

Output: string
Argument: s (string)

Returns a copy of s in which any lower-case characters are converted to upper case.


tr

Output: scalar
Argument: A (square matrix)

Returns the trace of the square matrix A, that is, the sum of its diagonal elements. See also diag.


transp

Output: matrix
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'.


trimr

Output: matrix
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.

See also selifr.


typestr

Output: string
Argument: typecode (integer)

Returns the name of the gretl data-type corresponding to typecode. This is intended for use in conjunction with the function inbundle. The value returned is one of "scalar", "series", "matrix", "string", "bundle" or "null".


uniform

Output: series
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.


uniq

Output: column vector
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.


unvech

Output: square matrix
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.

See also mshape, vech.


upper

Output: square matrix
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.

See also lower.


urcpval

Output: scalar
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.

See also pvalue.


values

Output: column vector
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)).

See also uniq, dsort, sort.


var

Output: scalar or series
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 yt 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.

See also sd.


varname

Output: string
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.


varnum

Output: integer
Argument: varname (string)

Returns the ID number of the variable called varname, or NA is there is no such variable.


varsimul

Output: matrix
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 horizontal stacking of the Ai matrices; 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.

See also $compan, var, vecm.


vec

Output: column vector
Argument: X (matrix)

Stacks the columns of X as a column vector. See also mshape, unvech, vech.


vech

Output: column vector
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.


weekday

Output: integer
Arguments:year (integer)
month (integer)
day (integer)

Returns the day of the week (Sunday = 0, Monday = 1, etc.) for the date specified by the three arguments, or NA if the date is invalid.


wmean

Output: series
Arguments:Y (list)
W (list)

Returns a series y such that yt 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.

See also wsd, wvar.


wsd

Output: series
Arguments:Y (list)
W (list)

Returns a series y such that yt 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.

See also wmean, wvar.


wvar

Output: series
Arguments:X (list)
W (list)

Returns a series y such that yt 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.

See also wmean, wsd.


xmax

Output: scalar
Arguments:x (scalar)
y (scalar)

Returns the greater of x and y, or NA if either value is missing.

See also xmin, max, min.


xmin

Output: scalar
Arguments:x (scalar)
y (scalar)

Returns the lesser of x and y, or NA if either value is missing.

See also xmax, max, min.


xpx

Output: list
Argument: L (list)

Returns a list that references the squares and cross-products of the variables in list L. Squares are named on the pattern sq_varname and cross-products on the pattern var1_var2. 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.


zeromiss

Output: same type as input
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.


zeros

Output: matrix
Arguments:r (integer)
c (integer)

Outputs a zero matrix with r rows and c columns. See also ones, seq.