Dynamic generalized extreme value modeling via particle filters

ABSTRACT

This article addresses how particle filters compare to MCMC methods for posterior density approximations of a model that allows for a dynamic state with fixed parameters and where the observation equation is nonlinear. This is a problem that was not been well studied in the specialized literature. We prove that these state and parameter estimations can be achieved via particle filter methods without the need of more expensive Forward Filtering Backward Sampling (FFBS) simulation. Estimation of a time-varying extreme value model via the generalized extreme value distribution is considered using these particle filter methods and compared to a MCMC algorithm that involves a variety of Metropolis-Hastings steps. We illustrate and compare the different methodologies with simulated data and some minimum daily stock returns occurring monthly from January 4, 1990 to December 28, 2007 using the Tokyo Stock Price Index (TOPIX).

KEYWORDS:

• GEV distribution
• MCMC
• Nonlinear observation
• Particle filters
• Topix dataset

MATHEMATICS SUBJECT CLASSIFICATION:

• 62 Statistics
• 62L Sequential methods
• 62L12 Sequential estimation

Acknowledgments

We thank the Editor and the Referee for their valuable comments that had helped us to improve previous versions of this article. This research was partially funded by the U.S. Department of Energy, Office of Science, Biological and Environmental Research, Award: DE-SC0010843.