Nonparametric estimation for high-frequency data incorporating trading information

We propose nonparametric estimators for the explicative part of the noise in a model where the market microstructure noise is an unknown function of the trading information while allowing for the presence of an additional residual noise component. Our method allows for dependence in the observable trading information and accommodates the presence of infinite variation jumps in the efficient price process. We establish the convergence and asymptotic normality of the proposed estimators. We also propose a two-step Laplace estimator of integrated volatility where we replace the observed price with the estimated price by removing the explicative part of the market microstructure noise. The finite sample properties of both the nonparametric estimators and the two-step Laplace estimator are examined through Monte Carlo simulations. We find that our method is robust to misspecification of the unknown functional form given finite sample size. Furthermore, an empirical application using high -frequency data demonstrates that our method outperforms commonly employed parametric methods.