Stationary bootstrap for kernel density estimators under psi-weak dependence
Stationary bootstrap technique is applied for kernel-type estimators of densities and their derivatives of stationary psi-weakly dependent processes. The psi-weak dependence, introduced by Doukhan & Louhichi [Doukhan, P., Louhichi, S., 1999. A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications 84,313-342], unifies weak dependence conditions such as mixing, association, Gaussian sequences and Bernoulli shifts. The class of psi-weakly dependent processes includes all weakly dependent processes of interest in statistics, containing such important processes as GARCH processes, threshold autoregressive processes, and bilinear processes. We obtain asymptotic validity for the stationary bootstrap in the density and derivatives estimation. A Monte-Carlo experiment compares the proposed method with other methods. Log returns of daily Dow Jones index are analyzed by the proposed method. (C) 2011 Elsevier B.V. All rights reserved.
stationary bootstrap density weak dependence derivative kernel estimator