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 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.
|Date of creation:||Jan 2011|
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- J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
- Toshiaki Watanabe, 2004. "A multi-move sampler for estimating non-Gaussian time series models: Comments on Shephard & Pitt (1997)," Biometrika, Biometrika Trust, vol. 91(1), pages 246-248, March.
- Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
- Fruhwirth-Schnatter, Sylvia & Fruhwirth, Rudolf, 2007. "Auxiliary mixture sampling with applications to logistic models," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3509-3528, April.
- Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
- Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
- Yasuhiro Omori & Toshiaki Watanabe, 2007.
"Block Sampler and Posterior Mode Estimation for Asymmetric Stochastic Volatility Models,"
CIRJE-F-507, CIRJE, Faculty of Economics, University of Tokyo.
- Omori, Yasuhiro & Watanabe, Toshiaki, 2008. "Block sampler and posterior mode estimation for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2892-2910, February.
- Sylvia FrüHwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, vol. 93(4), pages 827-841, December.
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