Parametric Inference for Nonsynchronously Observed Diffusion Processes in the Presence of Market Microstructure Noise

TL;DR

This paper develops a new statistical method for estimating parameters of diffusion processes from irregular, noisy market data, demonstrating asymptotic properties and improved quadratic covariation estimation.

Contribution

It introduces a quasi-likelihood approach for nonsynchronous, noisy observations and proves its asymptotic efficiency and normality under certain conditions.

Findings

Estimator exhibits asymptotic mixed normality.

Proved local asymptotic normality and efficiency.

Numerical results show improved quadratic covariation estimation.

Abstract

We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of maximum-likelihood- and Bayes-type estimators based on it. We also prove the local asymptotic normality of the model and asymptotic efficiency of our estimator when the diffusion coefficients are constant and noise follows a normal distribution. We conjecture that our estimator is asymptotically efficient even when the latent process is a general diffusion process. An estimator for the quadratic covariation of the latent process is also constructed. Some numerical examples show that this estimator performs better compared to existing estimators of the quadratic covariation.