Parameter estimation for threshold Ornstein-Uhlenbeck processes from discrete observations

TL;DR

This paper develops consistent and asymptotically normal estimators for parameters of threshold Ornstein-Uhlenbeck processes based on discrete observations, utilizing ergodic theory and explicit invariant measures.

Contribution

It introduces generalized moment estimators for threshold Ornstein-Uhlenbeck processes and proves their strong consistency and asymptotic normality.

Findings

Estimators are strongly consistent as sample size increases.

Estimators are asymptotically normal.

Explicit invariant measure is derived for the process.

Abstract

Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we need to find the explicit form of the invariant measure. With the sampling time step arbitrarily fixed, we prove the strong consistency and asymptotic normality of our estimators as the sample size tends to infinity.