Kalman

Kalman — The Kalman filter

Functions

Types and Values

typedef kalman

Object Hierarchy


Includes

#include <gretl/libgretl.h>
#include <gretl/kalman.h>

Description

Functions

kalman_new ()

kalman *
kalman_new (const gretl_matrix *S,
            const gretl_matrix *P,
            const gretl_matrix *F,
            const gretl_matrix *A,
            const gretl_matrix *H,
            const gretl_matrix *Q,
            const gretl_matrix *R,
            const gretl_matrix *y,
            const gretl_matrix *x,
            const gretl_matrix *m,
            gretl_matrix *E,
            int *err);

Allocates and initializes a Kalman struct, which can subsequently be used for forecasting with kalman_forecast(). The nomenclature for the various required matrices is that in Hamilton's Time Series Analysis (1994, chapter 13), except that "S" is used in place of Hamilton's \xi for the state vector.

Parameters

S

r x 1 initial state vector.

 

P

r x r initial precision matrix.

 

F

r x r state transition matrix.

 

A

n x k matrix of coefficients on exogenous variables in the observation equation.

 

H

n x r matrix of coefficients on the state variables in the observation equation.

 

Q

r x r contemporaneous covariance matrix for the errors in the state equation.

 

R

n x n contemporaneous covariance matrix for the errors in the observation equation (or NULL if this is not applicable).

 

y

T x n matrix of dependent variable(s).

 

x

T x k matrix of exogenous variable(s). May be NULL if there are no exogenous variables, or if there's only a constant.

 

m

r x 1 vector of constants in the state transition, or NULL.

 

E

T x n matrix in which to record forecast errors (or NULL if this is not required).

 

err

location to receive error code.

 

Returns

pointer to allocated struct, or NULL on failure, in which case err will receive a non-zero code.


kalman_free ()

void
kalman_free (kalman *K);


kalman_forecast ()

int
kalman_forecast (kalman *K,
                 PRN *prn);

Generates a series of one-step ahead forecasts for y, based on information entered initially using kalman_new(), and possibly modified using kalman_set_initial_state_vector() and/or kalman_set_initial_MSE_matrix(). The log-likelihood is calculated for the sequence of forecast errors on the assumption of normality: this can be accessed using kalman_get_loglik().

Parameters

K

pointer to Kalman struct: see kalman_new().

 

prn

printing apparatus (or NULL).

 

Returns

0 on success, non-zero on error.


kalman_get_loglik ()

double
kalman_get_loglik (const kalman *K);

Retrieves the log-likelhood calculated via a run of kalman_forecast().

Parameters

K

pointer to Kalman struct.

 

Returns

ll value, or NADBL on failure.


kalman_get_arma_variance ()

double
kalman_get_arma_variance (const kalman *K);

Retrieves the estimated variance for an ARMA model estimated using the Kalman filter.

Parameters

K

pointer to Kalman struct.

 

Returns

sigma-squared value, or NADBL on failure.


kalman_arma_smooth ()

gretl_matrix *
kalman_arma_smooth (kalman *K,
                    int *err);

Runs a filtering pass followed by a smoothing pass.

Parameters

K

pointer to Kalman struct.

 

err

location to receive error code.

 

Returns

matrix containing the smoothed estimate of the dependent variable, or NULL on error.


kalman_smooth ()

gretl_matrix *
kalman_smooth (kalman *K,
               gretl_matrix **pP,
               gretl_matrix **pU,
               int *err);

Runs a filtering pass followed by a backward, smoothing pass. At present the pU argument is experimental and a bodge: it will not actually do anything unless pP is left NULL.

Parameters

K

pointer to kalman struct.

 

pP

pointer to matrix in which to retrieve the MSE of the smoothed state (or NULL if this is not required).

 

pU

pointer to matrix in which to retrieve the smoothed disturbances (or NULL if this is not required).

 

err

location to receive error code.

 

Returns

matrix containing the smoothed estimate of the state, or NULL on error.


kalman_set_initial_state_vector ()

int
kalman_set_initial_state_vector (kalman *K,
                                 const gretl_matrix *S);

Resets the initial value of the state vector in a Kalman struct, using the values from S . See also kalman_new().

Parameters

K

pointer to Kalman struct.

 

S

matrix of values to set.

 

Returns

0 on success, non-zero on error.


kalman_set_initial_MSE_matrix ()

int
kalman_set_initial_MSE_matrix (kalman *K,
                               const gretl_matrix *P);

Resets the initial value of the MSE matrix in a Kalman struct, using the values from P . See also kalman_new().

Parameters

K

pointer to Kalman struct.

 

P

matrix of values to set.

 

Returns

0 on success, non-zero on error.


kalman_set_nonshift ()

void
kalman_set_nonshift (kalman *K,
                     int n);


kalman_set_options ()

void
kalman_set_options (kalman *K,
                    int opts);


kalman_get_options ()

int
kalman_get_options (kalman *K);

Returns


kalman_attach_data ()

void
kalman_attach_data (kalman *K,
                    void *data);


kalman_get_data ()

void *
kalman_get_data (const kalman *K);

Returns


kalman_attach_printer ()

void
kalman_attach_printer (kalman *K,
                       PRN *prn);


kalman_get_printer ()

PRN *
kalman_get_printer (const kalman *K);

Returns

Types and Values

kalman

typedef struct kalman_ kalman;