Efficient estimation and particle filter for max-stable processes. (English) Zbl 1300.62094
Summary: 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.
MSC:
| 62M20 | Inference from stochastic processes and prediction |
| 60G70 | Extreme value theory; extremal stochastic processes |
| 60G52 | Stable stochastic processes |
| 62F15 | Bayesian inference |
| 60J22 | Computational methods in Markov chains |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 91G70 | Statistical methods; risk measures |
| 91B84 | Economic time series analysis |
Keywords:
Bayesian analysis; extreme value theory; Markov chain Monte Carlo; marginal likelihood; maxima of moving maxima processes; stock returnsSoftware:
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