Journal
JOURNAL OF TIME SERIES ANALYSIS
Volume 33, Issue 1, Pages 61-80Publisher
WILEY
DOI: 10.1111/j.1467-9892.2011.00740.x
Keywords
Bayesian analysis; extreme value theory; Markov chain Monte Carlo; marginal likelihood; maxima of moving maxima processes; stock returns
Funding
- Japanese Ministry of Education, Science, Sports, Culture and Technology [21243018]
- Japan Society for the Promotion of Science
- Nakajima Foundation
- NSF [DMS-0804575]
- Grants-in-Aid for Scientific Research [21243018, 22300097] Funding Source: KAKEN
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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.
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