Quasi-likelihood analysis for nonlinear stochastic processes

Abstract

A brief overview of the theory of quasi-likelihood analysis (QLA) is given and its usefulness is demonstrated with applications to estimation for a volatility parameter of a semimartingale. A simplified version of the QLA is recalled. The role of non-degeneracy of a key index reflecting identifiability is highlighted. In an application of the QLA, the concept of global jump filters is introduced for precise estimation of the volatility parameter from the data contaminated with jumps.