vgxloglik - Loglikelihoods of multivariate time series process

Synopsis

LLF = vgxloglik(Spec,W)

[LLF,CLLF] = vgxloglik(Spec,W)

Description

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`.

Example

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

load vgxexample Spec Y Y0 W0

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)

LLF =

   17.8440