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

Jouchi Nakajima, Tsuyoshi Kunihama, Yasuhiro Omori () and Sylvia Frühwirth-Schnatter

Computational Statistics & Data Analysis, 2012, vol. 56, issue 11, 3241-3259

Abstract: 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.

Keywords: Extreme values; Generalized extreme value distribution; Markov chain Monte Carlo; Mixture sampler; State space model; Stock returns (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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Related works:
Working Paper: Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:11:p:3241-3259

DOI: 10.1016/j.csda.2011.04.017

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