The non-parametric estimation of volatility in high frequency data and its bandwidth selection

The non-parametric estimator of volatility based on high frequency data is the current focus due to its high accuracy. All of these estimator have to choose their optimal bandwidth in the application. However, it is difficult to calculate the optimal bandwidth from the real data and to apply these estimator, since optimal bandwidth always take some awkward unknown parameters. In this paper, taking realized kernel as the representative, a new data-driven algorithm for selecting the bandwidth has been constructed. The stability of algorithm is proved and the selected bandwidth is consistent estimator of optimal bandwidth without bias. The convergence rate is O(n^-1/5). It is shown from the numerical examples that the algorithm is adaptive and the finally selected bandwidth is independent on the original value. Simulation result shows that the estimator for volatility with bandwidth selected by our algorithm has higher accuracy. The proposed algorithm could be modified to select optimal bandwidth for other non-parametric estimator of volatility as well.