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.