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 Fruwirth-Scnatter
Additional contact information
Sylvia Fruwirth-Scnatter: Professor, Department of Applied Statistics, Johannes Kepler University in Lintz. (E-mail: Sylvia.Fruehwirth-Schnatter@jku.at)

No 09-E-32, IMES Discussion Paper Series from Institute for Monetary and Economic Studies, Bank of Japan

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 a very 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 for 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)
JEL-codes: C11 C51 G17 (search for similar items in EconPapers)
Date: 2009-11
New Economics Papers: this item is included in nep-ecm, nep-ets, nep-ore and nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Generalized extreme value distribution with time-dependence using the AR and MA models in state space form (2012)
Working Paper: Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form (2011)
Working Paper: Generalized extreme value distribution with time-dependence using the AR and MA models in state space form (2009)
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