Title: Global jump filters and quasi likelihood analysis for volatility
Authors: Nakahiro Yoshida - University of Tokyo (Japan) [presenting]
Abstract: New estimation schemes for volatility parameters of a semimartingale with jumps are proposed. In order to detect jumps, construction of a suitable filter that correctly discriminates intervals having jumps among all observation intervals is critical. The jump-filters proposed so far are based on time-locally constructed tests of jumps, and they suffer restrictions on the distribution of jumps. The proposed jump-filters take advantage of global information in the data to detect jumps more accurately. The quasi likelihood analysis (QLA) for volatility parameter estimation is formulated by using the newly proposed jump filters. Stable convergence to a mixed normal distribution of the QLA estimators (the quasi maximum likelihood estimator and the quasi Bayesian estimator) and moment convergence of the error are established. Numerical simulations show that our global method obtains better estimates of the volatility parameter than the previous local method.