vgxplot plots a multivariate time series
process with optional error bands.

Required Input Arguments

Spec

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

Y

nPY observed paths of an n-dimensional
time series process with T observations for each
path, collected in a T-by-n-by-nPY array.
Times are ordered by row from oldest to most recent. Plotted error
bands are plus or minus one standard deviation of the one-period prediction
error derived from Spec.

Optional Input Arguments

FY

nPFY forecast paths of an n-dimensional
time series process with FT observations for each
path, collected in a FT-by-n-by-nPFY array.
Times are ordered by row from oldest to most recent. Plotted error
bands are plus or minus one standard deviation of the cumulative forecast
error derived from FYCov.

FYCov

A single path of forecast error covariances for an n-dimensional
time series process with FT observations. FYCov is
stored as an FT-cell vector with n-by-n forecast
error covariance matrices in each cell for FT times. FYCov is
the same if the underlying time series process has multiple paths,
so only one path is necessary. Although multiple time series paths
can be plotted, FYCov is based on calibration of
a single path of the time series process. Plots with multiple forecast
paths are displayed with error bands derived from FYCov that
may not be valid for all paths. Nonetheless, the error bands enclose
the envelope of multiple paths.

Examples

Forecast and Plot a Vector Autoregressive Process

Start with a 2-dimensional VARMA(2, 2) specification structure
in Spec and time series data in Y:

load Data_VARMA22

Propagate the time series forward 5 periods in FY and
the forecast error covariance in FYCov:

[FY, FYCov] = vgxpred(Spec, 5, [], Y);

Plot just the times series process with 1-step prediction error
bands:

vgxplot(Spec, Y);

Plot just the forecast time series process with t-step
prediction error bands:

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

Plot both the time series process and its forecast with prediction
errors (here the plot just displays the last 10 samples of the times
series data):