Time endogeneity and an optimal weight function in pre-averaging covariance estimation

TL;DR

This paper proves a central limit theorem for pre-averaging covariance estimators under endogenous observation times, showing that certain functionals mitigate endogeneity effects and discussing optimal weight functions.

Contribution

It establishes a central limit theorem in a general endogenous time setting and identifies conditions under which endogeneity does not affect asymptotic distribution.

Findings

Endogeneity has no impact on the asymptotic distribution under certain conditions.

Optimal weight functions can be chosen to improve estimation.

Contrasts with realized volatility in pure diffusion models.

Abstract

We establish a central limit theorem for a class of pre-averaging covariance estimators in a general endogenous time setting. In particular, we show that the time endogeneity has no impact on the asymptotic distribution if certain functionals of observation times are asymptotically well-defined. This contrasts with the case of the realized volatility in a pure diffusion setting. We also discuss an optimal choice of the weight function in the pre-averaging.