Likelihood-Based Inference in Autoregressive Models with Scaled t-Distributed Innovations by Means of EM-Based Algorithms

Abstract

This article applies the EM-based (ECM and ECME) algorithms to find the maximum likelihood estimates of model parameters in general AR models with independent scaled t-distributed innovations whenever the degrees of freedom are unknown. The ECME, sharing advantages with both EM and Newton–Raphson algorithms, is an extension of ECM, which itself is an extension of the EM algorithm. The ECM and ECME algorithms, which are analytically quite simple to use, are then compared based on the computational running time and the accuracy of estimation via a simulation study. The results demonstrate that the ECME is efficient and usable in practice. We also show how our method can be applied to the Wolfer's sunspot data.

Keywords:

• Autoregressive process
• ECM algorithm
• ECME algorithm
• EM algorithm
• t-distribution

Mathematics Subject Classification:

• 62M10
• 37M10

Acknowledgments

The authors express their sincere thanks to the editor and referee(s) for providing valuable comments and suggestions.