vgxloglik computes total and conditional
loglikelihoods of a multivariate time series process.

Input Arguments

Spec

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

W

Innovations process. nP paths of an n-dimensional
innovations process with T observations for each
path, collected in a T-by-n-by-nP array.
Times are ordered by row from oldest to most recent. The innovations
covariance is assumed to be positive-definite. To obtain innovations
given a specification structure and a path of a multiple time series
process, use vgxinfer.

Output Arguments

LLF

Total loglikelihood function for T observations
of an n-dimensional time series process. If W has nP paths, LLF is
a 1-by-nP vector containing the total loglikelihood
function for each path.

CLLF

Conditional loglikelihoods for T observations
of an n-dimensional time series process. If W has nP paths, CLLF is
a T-by-nP matrix containing
the conditional loglikelihoods for each path. The total loglikelihood LLF is
the sum of the T conditional loglikelihoods in CLLF.

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

load Data_VARMA22

Compute the total loglikelihood function given a specification structure in Spec and an innovations process derived from the time series data Y using the function vgxinfer:

W = vgxinfer(Spec, Y, [], Y0, W0);
LLF = vgxloglik(Spec, W)