  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.
