Abstract #301051

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JSM 2003 Abstract #301051
Activity Number: 162
Type: Topic Contributed
Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #301051
Title: Estimation of M4 Processes with Particle Filters
Author(s): Francisco Chamu*+ and Richard L. Smith
Companies: University of North Carolina, Chapel Hill and University of North Carolina
Address: Department of Statistics, UNC-CH, Chapel Hill, NC, 27599-3260,
Keywords: multivariate extreme value theory ; max-stable processes ; M4 processes ; Bayesian analysis ; particle filters
Abstract:

Multivariate extreme value theory is concerned with the joint distribution of extremes of multiple random variables. The theory is used in a number of areas such as finance and environmental science. For example, empirical observations suggest that extreme events in financial time series occur in clusters and are dependent across different assets. It is possible to characterize a multivariate stationary time series in terms of a limiting max-stable process. Our approach for the statistical modeling of max-stable processes is based on Multivariate Maxima of Moving Maxima (M4) processes. However, the joint densities of M4 processes contain singularities because of the presence of deterministic signature patterns, so it is not possible to apply the method of maximum likelihood to estimate the parameters of the model. We propose Bayesian estimation of M4 processes using a class of simulation filters known as particle filters. We illustrate the method with stock returns data, and show an application to the estimation of tail-related measures of risk, such as Value at Risk (VaR).

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