Extreme Value Autoregressive Model and Its Applications

Abstract

This article proposes a first-order autoregressive model with Gumbel extreme value marginal distribution to analyze the time-series data. As the innovation distribution of the model does not admit a closed-form expression, the problem of estimation becomes complicated. In this article, we propose the method of conditional least squares, quasi maximum likelihood, and maximum likelihood for estimating model parameters. Simulation studies are carried out to assess the performance of these methods. Two sets of real data are analyzed to illustrate the applications of the proposed model.

AMS Subject Classification:

• 62M10

Keywords:

• Autoregressive models
• Conditional least squares method
• Gumbel extreme value distribution
• Maximum likelihood method
• Quasi maximum likelihood method

Acknowledgments

The authors thank the referees for their constructive comments on an earlier version of the article.

Funding

This research was partially supported by SERC scheme of the Department of Science and Technology, Government of India, through a research grant, number SR/S4/MS:522/08.