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Seminar on Probability and Statistics Tuesday May 12 2009 Tokyo 126 4:20-5:30 pm
Asymptotically efficient estimation of multiple change points in GARCH types models
塩濱 敬之 / SHIOHAMA Takayuki 東京理科大学, 工学部 / Tokyo University of Science, Department of Management Science Abstract Instability of volatility parameters in GARCH models in an important
issue for analyzing financial time series. In this paper we investigate
the asymptotic theory for multiple change point estimators of
GARCH$(p,q)$ models. When the parameters of a GARCH models have changed
within an observed realization, two types estimators, Maximum likelihood
estimator (MLE) and Bayesian estimator (BE), are proposed. Then we
derive the asymptotic distributions for these estimators. The MLE and
BE have different limit laws, and the BE is asymptotically
efficient. Monte Carlo studies on the finite sample behaviors are
conducted. Applications to Nikkei 225 index are discussed.
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