Parameter estimation and model testing for Markov processes via conditional characteristic functions

TL;DR

This paper introduces an empirical likelihood method utilizing conditional characteristic functions for parameter estimation and model testing in Markov processes, applicable to both continuous and jump processes, with theoretical validation and empirical demonstrations.

Contribution

It develops a novel empirical likelihood framework based on conditional characteristic functions for Markov process analysis, including parameter estimation and model specification testing.

Findings

The proposed estimator is consistent and asymptotically normal.

The empirical likelihood ratio test effectively distinguishes correct model specifications.

Simulation and case studies confirm the method's practical effectiveness.

Abstract

Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for L\'{e}vy-driven processes. We propose an empirical likelihood approach, for both parameter estimation and model specification testing, based on the conditional characteristic function for processes with either continuous or discontinuous sample paths. Theoretical properties of the empirical likelihood estimator for parameters and a smoothed empirical likelihood ratio test for a parametric specification of the process are provided. Simulations and empirical case studies are carried out to confirm the effectiveness of the proposed estimator and test.