Asymptotic Fisher information matrix of Markov switching VARMA models

We study the Fisher information (FI) matrix of Markov switching vector autoregressive moving average (MS VARMA) models and derive an explicit expression in closed form for the asymptotic FI matrix of the underlying model. Our result is more general than the available one in the literature for linear VARMA models, which has been recently studied in Bao and Hua (2014), in two respects. First, we treat the variance of the error term in a more general setting rather than considering it as a nuisance parameter. Then, we consider non-trivial intercept in the MS VARMA model. Under general conditions, the asymptotic FI matrix can be used to derive the asymptotic covariance matrix of the Gaussian maximum likelihood estimator of the model parameters. Some examples and numerical applications illustrate the results.