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Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form
Nakajima, Jouchi
98662
Kunihama, Tsuyoshi
98663
Omori, Yasuhiro
98664
Frühwirth-Schnatter, Sylvia
98665
335
Extreme values
Generalized extreme value distribution
Markov chain
Monte Carlo
Mixture sampler
State space model
Stock returns
application/pdf
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 fol- low 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 accu- rate 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 tted to a monthly series of minimum returns and the empirical results support strong evidence of time-dependence among the observed minimum returns
Revised version of CIRJE-F-689 (2009); subsequently published in Computational Statistics and Data Analysis, 56-11, 3241-3259. November 2012.
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technical report
日本経済国際共同センター
2011-01
Discussion paper series. CIRJE-F
CIRJE-F-782
AA11450569
eng
http://www.cirje.e.u-tokyo.ac.jp/research/dp/2011/2011cf782ab.html
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