A markovian local resampling scheme for nonparametric estimators in time series analysis

Abstract

In this paper we study the properties of a pth-order Markovian local resampling procedure in approximating the distribution of nonparametric (kernel) estimators of the conditional expectation m(x

φ) = E(φ(X t+1)|Y t,p = x) where {X t,t ≥ 1} is a strictly stationary process, Y t,p = (X t,X t-1,..., X t-p+1) τ, and φ(·) is a measurable real-valued function. Under certain regularity conditions, asymptotic validity of the proposed resampling scheme is established for a class of stochastic processes that is broader than the class of stationary Markov processes. Some simulations illustrate the finite sample performance of the proposed resampling procedure.