LAN property for an ergodic Ornstein-Uhlenbeck process with Poisson jumps

TL;DR

This paper establishes the local asymptotic normality of an ergodic Ornstein-Uhlenbeck process with jumps, observed at high frequency, using advanced stochastic calculus techniques to facilitate statistical inference for unknown parameters.

Contribution

It derives the LAN property for a jump-diffusion process with unknown parameters, employing Malliavin calculus and Girsanov's theorem in a high-frequency observation setting.

Findings

LAN property established for the process

Methodology applicable to high-frequency data analysis

Facilitates statistical inference for jump-diffusion models

Abstract

In this paper, we consider an ergodic Ornstein-Uhlenbeck process with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its jump intensity depend on unknown parameters. Considering the process discretely observed at high frequency, we derive the local asymptotic normality property. To obtain this result, Malliavin calculus and Girsanov's theorem are applied to write the log-likelihood ratio in terms of sums of conditional expectations, for which a central limit theorem for triangular arrays can be applied.