Seminars 2008 — Abstracts

Friday, February 22

Speaker: Song Chen, Iowa State University

Title: Parameter Estimation and Model Testing Based on Conditional Characteristic Functions for Continuous-Time Markov Processes

Abstract: We consider parameter estimation and testing for model specification for parametric Markov processes defined by stochastic differential equations. The processes more often admit close-form expressions for their conditional characteristic functions while their transitional densities are not explicitly available. hese processes includes continuous-time Brownian motion driven or Levy driven processes, which allow either continuous and discontinuous sample paths respectively. An empirical likelihood estimator for the parameter of the process, and an empirical likelihood ratio test for the parametric specification of the process are proposed. It is demonstrated that both the parameter estimation and the test enjoy good theoretical properties. Extensive simulations are carried out to confirm the effectiveness of the estimator and the tests in detecting jumps of finite activity and infinite activity respectively for some continuous-time Levy driven processes. We also conduct a case study on a Federal fund rate data and find there is a strong evidence for the presence of jumps.