vgxpred - Transient forecast response of multivariate time series process

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.

Example

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

load vgxexample Spec Y W

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);