Efficient Estimation and Particle Filter for Max‐Stable Processes
affiliation not provided to SSRN
University of Tokyo
Journal of Time Series Analysis, Vol. 33, Issue 1, pp. 61-80, 2012
Extreme values are often correlated over time, for example, in a financial time series, and these values carry various risks. Max‐stable processes such as maxima of moving maxima (M3) processes have been recently considered in the literature to describe time‐dependent dynamics, which have been difficult to estimate. This article first proposes a feasible and efficient Bayesian estimation method for nonlinear and non‐Gaussian state space models based on these processes and describes a Markov chain Monte Carlo algorithm where the sampling efficiency is improved by the normal mixture sampler. Furthermore, a unique particle filter that adapts to extreme observations is proposed and shown to be highly accurate in comparison with other well‐known filters. Our proposed algorithms were applied to daily minima of high‐frequency stock return data, and a model comparison was conducted using marginal likelihoods to investigate the time‐dependent dynamics in extreme stock returns for financial risk management.
Number of Pages in PDF File: 20
Keywords: Bayesian analysis, extreme value theory, Markov chain Monte Carlo, marginal likelihood, maxima of moving maxima processes, stock returns
JEL Classification: C11, C15, C51, C52, C58Accepted Paper Series
Date posted: December 28, 2011
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