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 Fruhwirth-Schnatter
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Sylvia Fruhwirth-Schnatter: Department of Applied Statistics, Johannes Kepler University in Lintz

No CIRJE-F-689, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

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.

Pages: 39 pages
Date: 2009-11
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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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