Robust estimation using multivariate t innovations for vector autoregressive models via ECM algorithm

ABSTRACT

This paper considers the vector autoregressive model of order p, VAR(p), with multivariate t error distributions, the latter being more prevalent in real life than the usual multivariate normal distribution. It is believed that the maximum-likelihood equations for the multivariate t distribution have convergence problem, hence we develop estimation procedures for VAR(p) model using the normal mean–variance mixture representation of multivariate t distribution. The procedure relies on the computational ease available in Expectation Maximization-based algorithms. The estimators obtained are explicit functions of sample observations and therefore are easy to compute. Extensive simulation experiments show that the estimators have negligible bias and are considerably more efficient than an existing method that uses the least-squares error approach. It is shown that the proposed estimators are robust to plausible deviations from an assumed distribution and hence are more advantageous when compared with the other estimator. One real-life example is given for illustration purposes.

Keywords:

• EM algorithms
• maximum likelihood estimation
• multivariate t distribution
• robust estimation
• vector autoregressive model

Disclosure statement

No potential conflict of interest was reported by the authors.