Bootstrapping stationary sequences by the Nadaraya-Watson regression estimator

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 (Kunsch, 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.