Exact Likelihood Equations for Autoregression Models with Multivariate Elliptically Contoured Distributions

Abstract

The multivariate elliptically contoured distributions provide a viable framework for modeling time-series data. It includes the multivariate normal, power exponential, t, and Cauchy distributions as special cases. For multivariate elliptically contoured autoregressive models, we derive the exact likelihood equations for the model parameters. They are closely related to the Yule-Walker equations and involve simple function of the data. The maximum likelihood estimators are obtained by alternately solving two linear systems and illustrated using the simulation data.

Keywords:

• Causality
• Covariance function
• Innovation distribution
• Kotz-type distribution
• Pearson-type VII distribution
• Stationary process
• Yule–Walker equations

Mathematics Subject Classification:

• 62M10
• 62E99