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Efficient estimation and particle filter for max‐stable processes

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  • Tsuyoshi Kunihama
  • Yasuhiro Omori
  • Zhengjun Zhang

Abstract

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 timedependent dynamics, which have been difficult to estimate. This paper 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.
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  • Tsuyoshi Kunihama & Yasuhiro Omori & Zhengjun Zhang, 2012. "Efficient estimation and particle filter for max‐stable processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(1), pages 61-80, January.
    • Handle: RePEc:bla:jtsera:v:33:y:2012:i:1:p:61-80
    DOI: j.1467-9892.2011.00740.x
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    Cited by:

    1. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori, 2017. "Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1248-1268, May.
    2. Wang, Yixin & So, Mike K.P., 2016. "A Bayesian hierarchical model for spatial extremes with multiple durations," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 39-56.
    3. Hee-Young Kim & Christian H. Weiß & Tobias A. Möller, 2020. "Models for autoregressive processes of bounded counts: How different are they?," Computational Statistics, Springer, vol. 35(4), pages 1715-1736, December.

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