Conditional Least Squares Estimation for Discretely Sampled Nonergodic Diffusions

Abstract

Strong consistency and conditional asymptotic normality of the conditional least squares estimator of a parameter appearing nonlinearly in the time dependent drift coefficient of the Itô stochastic differential equation are obtained under some regularity conditions when the corresponding diffusion is observed at discretely spaced dense time points satisfying a moderately increasing experimental design condition, the case of high frequency data. Main results are illustrated by the mean reversion process with drift and the nonhomogeneous Ornstein-Uhlenbeck process.