vgxpred

Forecast VARMAX model responses

Synopsis

FY = vgxpred(Spec,FT)

[FY,FYCov] = vgxpred(Spec,FT,FX,Y,W,NumPaths)

Description

vgxpred returns the transient response of a process during a forecast period with zero-valued innovations. To generate a process during a forecast period with simulated innovations, use vgxsim. To generate a process during a forecast period with known innovations, use vgxproc.

Input Arguments

Spec

A multivariate time series specification structure for an n-dimensional VARMA time series process, as created by vgxset.

FT

Number of forecast observations to be generated.

FX

nP paths of forecast regression design matrices associated with FT observations of an n-dimensional time series process, where each design matrix linearly relates nX exogenous inputs to each time series at each observation time. FX is an FT-by-nP matrix of cell arrays with n-by-nX design matrices in each cell. If FY has multiple paths, FX must contain either a single path or no fewer than the same number of paths as in FY. Extra paths are ignored.

Y

Presample time series process from the estimation period used for the forecast period. Y is a collection of nPY paths of an n-dimensional time series process with T observations for each path, collected in a T-by-n-by-nPY array. If Y has insufficient observations, the usual initialization methods for vgxproc and vgxsim apply.

W

Presample innovations process from the estimation period used for the forecast period. W is a collection of nPW paths of an n-dimensional innovations process with T observations for each path, collected in a T-by-n-by-nPW array. If W has insufficient observations, the usual initialization methods for vgxproc and vgxsim apply.

NumPaths

Number of paths to forecast. To generate multiple paths, you must use NumPaths to specify the number of paths. If FX, Y, and W have single paths and NumPaths > 1, every forecast is the same.

Output Arguments

FY

Forecast times-series process. FY is a collection of NumPaths paths of an n-dimensional time series process with FT observations for each path, collected in an FT-by-n-by-NumPaths array.

FYCov

Forecast error covariance matrices. FYCov is a single path of forecast error covariances for an n-dimensional time series process with FT observations. FYCov is collected in an FT-cell vector with n-by-n forecast error covariance matrices in each cell for t = 1, ..., FT. FYCov{1} is the one-period forecast covariance, FYCov{2} is the two-period forecast covariance, and so forth. FYCov is the same if multiple paths exist for the underlying time series process.

Examples

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Plot VARMA Model Forecasts

Start with a 2-dimensional VARMA(2, 2) specification structure in Spec and times series and innovations process in Y and W:

load Data_VARMA22

Forecast 10 samples into the future and use the time series and innovations process as presample data:

[FY, FYCov] = vgxpred(Spec, 10, [], Y, W);

Plot the transient response along with the predict-ahead forecast errors which are extracted from FYCov by the function vgxplot:

vgxplot(Spec, [], FY, FYCov);

See Also

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