Global jump filters and quasi-likelihood analysis for volatility


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 the 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 the 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” methods.

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The authors thank the reviewers for their valuable comments to improve this article.

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Correspondence to Nakahiro Yoshida.

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This work was in part supported by CREST JPMJCR14D7 Japan Science and Technology Agency; Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research No. 17H01702 (Scientific Research); and a Cooperative Research Program of the Institute of Statistical Mathematics.

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Inatsugu, H., Yoshida, N. Global jump filters and quasi-likelihood analysis for volatility. Ann Inst Stat Math (2021).

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  • Volatility
  • Jump
  • Global filter
  • High-frequency data
  • Quasi-likelihood analysis
  • Stochastic differential equation
  • Order statistic
  • Asymptotic mixed normality
  • Polynomial-type large deviation
  • Moment