Recursive nonparametric estimation for time series

Abstract:

Online or recursive estimation is natural for forecasting, and is computationally attractive by fast real-time updates when a new data item becomes available. In this talk we consider online kernel estimation for general time series models that satisfy the predictive dependence measure of Wu (2005). For a large class of stationary time series that are short- and long-range dependent, we will study the asymptotic properties for both the recursive density and the recursive regression estimators. We will characterize the asymptotic almost sure behaviors of the recursive estimators by deriving the sharp laws of the iterated logarithms, which are important for online procedures. We will also investigate the asymptotic normality, and the almost sure version of the optimal uniform convergence rates.