Statistical inference for ergodic diffusion with Markovian switching
Yuzhong Cheng, Hiroki Masuda
TL;DR
This work develops a Gaussian quasi-likelihood framework for estimating both the drift-diffusion parameters and the Markov-chain generator in ergodic diffusion models with Markovian regime switching, using high-frequency discrete observations. It proves consistency and asymptotic normality of the parameter estimators, and provides explicit, easily computable estimators for the generator $Q$. An OU-switching diffusion serves as a detailed example, with closed-form estimators and explicit asymptotic information in the two-state case. A separate quasi-likelihood approach yields a consistent estimator for $Q$ from the observed regime sequence alone, and extensive simulations illustrate finite-sample performance and confirm theoretical results. The methods offer practical inference tools for switching-diffusion models in applications spanning finance, ecology, and biology, under high-frequency sampling regimes where $T_n\to\infty$ and $n h_n^2\to 0$.
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.