Inference of online updating approach to nonparametric smoothing of big data

The online updating method (ONLINE) is an efficient analysis approach applied to big data. We prove the asymptotic properties and conduct statistical inference of the ONLINE models in kernel density and kernel regression. Several algorithms are proposed to solve the problems of the bandwidth selection in kernel density and regression respectively. We verify the asymptotic normality of the ONLINE density model in simulation and apply the ONLINE linear kernel regression to the Volatility Index (VIX) prediction. The empirical results show that the ONLINE linear kernel regression model achieves a comparable performance in continuously arriving option data streams prediction with significantly lower complexity than the classical local linear regression model.