VARMAX model loglikelihoods
LLF = vgxloglik(Spec,W)
[LLF,CLLF] = vgxloglik(Spec,W)
vgxloglik computes total and conditional loglikelihoods of a multivariate time series process.
A multivariate time series specification structure for an n-dimensional time series process, as created by vgxset.
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.
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.
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:
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