Testing if the market microstructure noise is fully explained by the informational content of some variables from the limit order book

TL;DR

This paper develops tests to determine if residual market microstructure noise exists beyond what can be explained by variables from the limit order book, using quasi-maximum likelihood estimators and a nonparametric framework.

Contribution

It introduces a novel testing methodology for residual noise in market microstructure models based on comparing two estimators within a nonparametric setting.

Findings

Tests can detect residual noise beyond known variables

Theoretical properties of estimators are established in a nonparametric framework

Central limit theorems are derived for the estimators in the presence of residual noise

Abstract

In this paper, we build tests for the presence of residual noise in a model where the market microstructure noise is a known parametric function of some variables from the limit order book. The tests compare two distinct quasi-maximum likelihood estimators of volatility, where the related model includes a residual noise in the market microstructure noise or not. The limit theory is investigated in a general nonparametric framework. In the presence of residual noise, we examine the central limit theory of the related quasi-maximum likelihood estimation approach.