Parameter estimation for ergodic linear SDEs from partial and discrete observations

TL;DR

This paper develops a quasi-likelihood estimator for unknown parameters in linear stochastic differential equations driven by an unobservable Ornstein-Uhlenbeck process, analyzing its asymptotic properties.

Contribution

It introduces a novel quasi-likelihood estimation method for partially observed ergodic linear SDEs and establishes its asymptotic behavior.

Findings

Consistent estimation of parameters from partial observations

Asymptotic normality of the estimator

Applicability to ergodic linear SDEs

Abstract

We consider a problem of parameter estimation for the state space model described by linear stochastic differential equations. We assume that an unobservable Ornstein-Uhlenbeck process drives another observable process by the linear stochastic differential equation, and these two processes depend on some unknown parameters. We construct the quasi-likelihood estimator (QMLE) of the unknown parameters and show asymptotic properties of the estimator.