"Generalized extreme value distribution with time-dependence using the AR and MA models in state space form"
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.
Year of publication: |
2009-11
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Authors: | Nakajima, Jouchi ; Kunihama, Tsuyoshi ; Omori, Yasuhiro ; Fruhwirth-Schnatter, Sylvia |
Institutions: | Center for International Research on the Japanese Economy (CIRJE), Faculty of Economics |
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