Classical and Bayes Analyses of Autoregressive Model with Heavy-Tailed Error

Abstract

This paper provides the classical and Bayesian analyses of autoregressive model having heavy-tailed errors’ distribution. We have considered a nonstandardized Student’s-t distribution for the independently and identically distributed error components. To proceed for the analyses, under the two paradigms, an appropriate selection of model has been done on the basis of Akaike information criterion and modified Bayesian information criterion respectively in the two said paradigms. The classical study mostly relies on the maximum likelihood estimates whereas for the Bayesian analysis, the posterior estimates are obtained, on the basis of some suitably chosen prior distributions for the parameters, by using the Markov chain Monte Carlo technique. The complete procedure is illustrated by the simulation study and a real dataset on GDP growth rate of India. The retrospective predictions have been made under the two paradigms separately. Since, the Bayesian estimates outperformed the classical estimates (in retrospective prediction), therefore, the prospective predictions are made under the Bayesian setup only. Such a study is expected to add a little contribution in the process of strategy making of the managerial bodies and further to encourage the researchers to come across an appropriate decisions.

KEYWORDS AND PHRASES:

• AIC and BIC
• GDP growth rate
• heavy-tailed autoregressive model
• MCMC
• metropolis algorithm
• retrospective and prospective predictions

Acknowledgements

The authors wish to express their thankfulness to the Editor-in-Chief and the anonymous referees for their valuable comments and suggestions that improved the earlier version of the manuscript.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Data and Code Availability Statement

The authors confirm that the data supporting the findings of this study are available within the article. The exemplary source codes are provided at GitHub in the following link: https://github.com/praveen2088/praveen2088/blob/main/Rcode_heavytailedAR.md.