Parameter estimation and model testing for Markov processes via conditional characteristic functions. (English) Zbl 1259.62069

Chen, Song X.; Peng, Liang; Yu, Cindy L.

Bernoulli 19, No. 1, 228-251 (2013).

Summary: 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 Lévy-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.

MSC:

62M05	Markov processes: estimation; hidden Markov models
62M02	Markov processes: hypothesis testing
60E10	Characteristic functions; other transforms
62G05	Nonparametric estimation
65C60	Computational problems in statistics (MSC2010)

Keywords:

diffusion processes; empirical likelihood; kernel smoothing; Lévy-driven processes

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