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

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.