In this paper, we build tests for the presence of error in a model where the market microstructure noise is a known parametric function of  the limit order book. The tests compare two novel and distinct quasi-maximum likelihood estimators of volatility, where the related model includes an additive error in the market microstructure noise or not. The limit theory is investigated in a general nonparametric framework. When there is no error in the model, following a common procedure, we provide a consistent estimator of the efficient price based on maximum likelihood estimation of the parameter. Furthermore, we show that realized volatility remains efficient when performed on the estimated price rather than on the efficient price .
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 .
R
error
residual noise
A
some variables from
D
novel and
R
an additive error
a residual noise
R
When there is no error in the model, following a common procedure, we provide a consistent estimator of the efficient price based on maximum likelihood estimation of the parameter. Furthermore, we show that realized volatility remains efficient when performed on the estimated price rather than on the efficient price
In the presence of residual noise, we examine the central limit theory of the related quasi-maximum likelihood estimation approach