Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike


14:30-15:30   Room #Zoom (Graduate School of Math. Sci. Bldg.)
Register at least 3 days before at the reference URL. The URL for participation sent before the seminar.
Nakahiro Yoshida (University of Tokyo)
Quasi-likelihood analysis for stochastic differential equations: volatility estimation and global jump filters (ENGLISH)
[ Abstract ]
Asia-Pacific Seminar in Probability and Statistics

The quasi likelihood analysis (QLA) is a framework of statistical inference for stochastic processes, featuring the quasi-likelihood random field and the polynomial type large deviation inequality. The QLA enables us to systematically derive limit theorems and tail probability estimates for the associated QLA estimators (quasi-maximum likelihood estimator and quasi-Bayesian estimator) for various dependent models. The first half of the talk will be devoted to an introduction to the QLA for stochastic differential equations. The second half presents recent developments in a filtering problem to estimate volatility from the data contaminated with jumps. A QLA for volatility for a stochastic differential equation with jumps is constructed, based on a "global jump filter" that uses all the increments of the process to decide whether an increment has jumps.

Key words: stochastic differential equation, high frequency data, Le Cam-Hajek theory, Ibragimov-Has'minskii-Kutoyants program, polynomial type large deviation inequality, quasi-maximum likelihood estimator, quasi-Bayesian estimator, L^p-estimates of the error, non-ergodic statistics, asymptotic (mixed) normality.
[ Reference URL ]