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Efficient estimation and particle filter for max‐stable processes
Author(s) -
Kunihama Tsuyoshi,
Omori Yasuhiro,
Zhang Zhengjun
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00740.x
Subject(s) - particle filter , maxima and minima , mathematics , markov chain monte carlo , maxima , bayesian probability , markov chain , gaussian , importance sampling , monte carlo method , algorithm , mathematical optimization , econometrics , statistics , kalman filter , art , mathematical analysis , physics , quantum mechanics , performance art , art history
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.