Gaussian and Student's $t$ mixture vector autoregressive model

A new mixture vector autoressive model based on Gaussian and Student's $t$ distributions is introduced. The G-StMVAR model incorporates conditionally homoskedastic linear Gaussian vector autoregressions and conditionally heteroskedastic linear Student's $t$ vector autoregressions as its mixture components, and mixing weights that, for a $p$th order model, depend on the full distribution of the preceding $p$ observations. Also a structural version of the model with time-varying B-matrix and statistically identified shocks is proposed. We derive the stationary distribution of $p+1$ consecutive observations and show that the process is ergodic. It is also shown that the maximum likelihood estimator is strongly consistent, and thereby has the conventional limiting distribution under conventional high-level conditions. Finally, this paper is accompanied with the CRAN distributed R package gmvarkit that provides easy-to-use tools for estimating the models and applying the methods.