Statistical inference for ergodic diffusion with Markovian switching

TL;DR

This paper develops a Gaussian quasi-likelihood method for estimating parameters in ergodic diffusion processes with Markovian switching, demonstrating asymptotic normality and providing a consistent estimator, supported by simulation results.

Contribution

It introduces a novel estimation approach for diffusion processes with Markovian switching, establishing asymptotic properties and a consistent estimator under ergodicity.

Findings

Asymptotic normality of estimators proven

Consistent estimator for Markov chain generator proposed

Simulation confirms theoretical results

Abstract

This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the unknown parameters contained in the drift and diffusion coefficients and present a consistent explicit estimator for the generator of the Markov chain. Simulation experiments are conducted to illustrate the theoretical results obtained.