vgxsim - Simulate multivariate time series process

Synopsis

Y = vgxsim(Spec,T)

[Y,W] = vgxsim(Spec,T,X,Y0,W0,NumPaths))

Description

vgxsim simulates a multivariate time series process.

Required Input Arguments

`Spec`	A multivariate time series specification structure for an n-dimensional time series process, as created by `vgxset`.
`T`	Number of observations to simulate.

Optional Input Arguments

`X`	Exogenous inputs. nPX paths of regression design matrices associated with T 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. `X` is a T-by-nPX matrix of cell arrays with n-by-nX design matrices in each cell. If `Y` has multiple paths, `X` must contain either a single path or no fewer than the same number of paths as in `Y`. Extra paths are ignored.
`Y0`	Presample time series process. nPY0 presample paths of an n-dimensional time series process with TY0 samples for each path, collected in a TY0-by-n-by-nPY0 array. If `Y0` is empty or if TY0 is less than the maximum AR lag in `Spec`, presample values are padded with zeros. If TY0 is greater than the maximum AR lag, the most recent samples from the last rows of each path of `Y0` are used. If `Y0` has multiple paths, `Y0` must contain either a single path or no fewer than the same number of paths as in `Y`. Extra paths are ignored.
`W0`	Presample innovations process. nPW0 presample paths of an n-dimensional innovations process with TW0 samples for each path, collected in a TW0-by-n-by-nPW0 array. If `W0` is empty or if TW0 is less than the maximum MA lag in `Spec`, presample values are padded with zeros. If TW0 is greater than the maximum MA lag, the most recent samples from the last rows of each path of `W0` are used. If `W0` has multiple paths, `W0` must contain either a single path or no fewer than the same number of paths as in `W`. Extra paths are ignored.
`NumPaths`	Number of paths to simulate. If `NumPaths` > 1, `X`, `Y0`, or `W0` must have either a single path or no fewer than `NumPaths` paths.

Output Arguments

`Y`	Time series process. `NumPaths` paths of an n-dimensional time series process with T observations for each path, collected in a T-by-n-by-`NumPaths` array. Times are ordered by row from oldest to most recent.
`W`	Innovations process. `NumPaths` paths of an n-dimensional innovations process with T observations for each path, collected in a T-by-n-by-`NumPaths` array. Times are ordered by row from oldest to most recent.

Example

Start with a 2-dimensional VARMA(2, 2) specification structure in Spec with presample data for the time series and innovations process:

load vgxexample Spec Y0 W0

Simulate 60 time steps of the time series process and plot the result:

Y = vgxsim(Spec, 60, [], Y0, W0);

vgxplot(Spec, Y);

Simulate 20 realizations of the time series process and plot the result:

Y = vgxsim(Spec, 60, [], Y0, W0, 20);

vgxplot(Spec, Y);