Generalized extreme value distribution with time-dependence using the AR and MA models in state space form

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• 作者：Jouchi Nakajima^a ; ^{jouchi.nakajima@stat.duke.edu} ; Tsuyoshi Kunihama^a ; ^{tsuyoshi.kunihama@stat.duke.edu} ; Yasuhiro Omori^b ; ^{omori@e.u-tokyo.ac.jp} ; Sylvia Frü ; hwirth-Schnatter^c ; ^{sylvia.fruehwirth-Schnatter@jku.at}
• 关键词：Extreme values ; Generalized extreme value distribution ; Markov chain Monte Carlo ; Mixture sampler ; State space model ; Stock returns
• 刊名：Computational Statistics and Data Analysis
• 出版年：2012
• 期刊代码：19_01679473
• 类别：cp
• 出版时间：November, 2012
• 卷：56
• 期：11
• 页码：3241-3259
• 文件大小：1072 K

摘要

A new state space approach is proposed to model the time-dependence in an extreme value process. The generalized extreme value distribution is extended to incorporate the time-dependence using a state space representation where the state variables either follow an autoregressive (AR) process or a moving average (MA) process with innovations arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm is proposed to implement Markov chain Monte Carlo method where we exploit an accurate approximation of the Gumbel distribution by a ten-component mixture of normal distributions. The methodology is illustrated using extreme returns of daily stock data. The model is fitted to a monthly series of minimum returns and the empirical results support strong evidence of time-dependence among the observed minimum returns.