Quotation Nakajima, Jouchi, Kunihama, Tsuyoshi, Omori, Yasuhiro, Frühwirth-Schnatter, Sylvia. 2012. Generalized extreme value distribution with time-dependence using the AR and MA models in state space form. Computational Statistics & Data Analysis 56 (11): 3241-3259.


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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.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Journal article
Journal Computational Statistics and Data Analysis
Citation Index SCI
WU-Journal-Rating new FIN-A, VW-D, WH-B
Language English
Title Generalized extreme value distribution with time-dependence using the AR and MA models in state space form
Volume 56
Number 11
Year 2012
Page from 3241
Page to 3259
URL http://www.sciencedirect.com/science/article/pii/S0167947311001460

Associations

People
Frühwirth-Schnatter, Sylvia (Details)
External
Kunihama, Tsuyoshi
Nakajima, Jouchi
Omori, Yasuhiro
Organization
Institute for Statistics and Mathematics IN (Details)
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