Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form
2010/08/03
研討會日期 : 2010-08-03
時間 : 14:00
主講人 : Professor Yasuhiro Omori
地點 : B110
演講者簡介 : Yasuhiro Omori got his Ph.D. in Statistics from University of Wisconsin at Madison in 1992. He is currently serving as Professor of Economics at University of Tokyo. His research interest is in statistics, econometrics and Markov Chain Monte Carlo method.
演講摘要 : 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.
