Bootstrapping stationary sequences by the Nadaraya-Watson regression estimator

Abstract

We propose a new bootstrap method for stationary time series data which uses the Nadaraya-Watson kernel regression estimator. We call this method N-W bootstrap. The N-W bootstrap consists of estimating the conditional autoregressive mean function by the Nadaraya-Watson estimator and bootstrapping the resulting residuals. Indeed we obtain a bootstrapped copy by regenerating a stationary time series data from the Nadaraya-Watson regression estimates and their bootstrapped residuals. A Monte Carlo simulation study is conducted to compare our method to the block bootstrap method (Ku¨nsch, 1989 or Liu and Singh, 1992) in various time series models, which shows the performance of the N-W bootstrap is better or at least comparable to the block bootstrap. Some practical usefulness of the N-W bootstrap is also discussed.