Parameter Estimation and Model Testing for Markov Processes via Conditional Characteristic Functions

Markov processes are used in a wide range of disciplines including finance. The transitional densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available especially for Lévy driven processes. We propose an empirical likelihood approach for estimation and model specification test based on the conditional characteristic function for processes whose sample paths can be either continuous or discontinuous with jumps. An empirical likelihood estimator for the parameter of a parametric process, and a smoothed empirical likelihood ratio test for the parametric specification of the process are proposed, which are shown to have good theoretical properties and empirical performance. Simulations and empirical case study are carried out to confirm the effectiveness of the estimator and the test. Keyword: Conditional characteristic function; Diffusion processes; Empirical likelihood; Kernel smoothing; Lévy driven processes Corresponding Author: Song X. Chen, Department of Statistics, Iowa State University, Ames, Iowa 50011-1210, USA. Tel: 1-515-2942729. Fax: 1-515-294 4040; Email: [email protected].