Testing if the market microstructure noise is a function of the limit order book. (arXiv:1709.02502v1 [q-fin.ST])

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, 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.