Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form
AbstractA 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.
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Bibliographic InfoPaper provided by Institute for Monetary and Economic Studies, Bank of Japan in its series IMES Discussion Paper Series with number 09-E-32.
Date of creation: Nov 2009
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Extreme values; Generalized extreme value distribution; Markov chain Monte Carlo; Mixture sampler; State space model; Stock returns;
Other versions of this item:
- 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, Elsevier, vol. 56(11), pages 3241-3259.
- Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori & Sylvia Fruhwirth-Schnatter, 2009. "Generalized extreme value distribution with time-dependence using the AR and MA models in state space form," CIRJE F-Series CIRJE-F-689, CIRJE, Faculty of Economics, University of Tokyo.
- Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori & Sylvia Fruhwirth-Schnatter, 2011. "Generalized Extreme Value Distribution with Time-Dependence Using the AR and MA Models in State Space Form," CIRJE F-Series CIRJE-F-782, CIRJE, Faculty of Economics, University of Tokyo.
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-11-27 (All new papers)
- NEP-ECM-2009-11-27 (Econometrics)
- NEP-ETS-2009-11-27 (Econometric Time Series)
- NEP-ORE-2009-11-27 (Operations Research)
- NEP-RMG-2009-11-27 (Risk Management)
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