Global jump filters and quasi likelihood analysis for volatility
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We propose a new estimation scheme for estimation of the volatility parameters of a semimartingale with jumps based on a jump-detection filter. Our filter uses all of data to analyze the relative size of increments and to discriminate jumps more precisely. We construct quasi maximum likelihood estimators and quasi Bayesian estimators, and show limit theorems for them including L^p-estimates of the error and asymptotic mixed normality based on the framework of quasi likelihood analysis. The global jump filters do not need a restrictive condition for the distribution of the small jumps. By numerical simulation we show that our "global" method obtains better estimates of the volatility parameter than the previous "local" method.
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