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

Jouchi Nakajima, Tsuyoshi Kunihama, Yasuhiro Omori, Sylvia Frühwirth-Schnatter

Publikation: Wissenschaftliche FachzeitschriftOriginalbeitrag in FachzeitschriftBegutachtung

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.
OriginalspracheEnglisch
Seiten (von - bis)3241 - 3259
FachzeitschriftComputational Statistics and Data Analysis
Jahrgang56
Ausgabenummer11
PublikationsstatusVeröffentlicht - 1 Aug. 2012

Zitat