Autoregressive-Aided Periodogram Bootstrap for Time Series

A bootstrap methodology for the periodogram of a stationary process is proposed which is based on a combination of a time domain parametric and a frequency domain nonparametric bootstrap. The parametric fit is used to generate periodogram ordinates that imitate the essential features of the data and the weak dependence structure of the periodogram while a nonparametric (kernel-based) correction is applied in order to catch features not represented by the parametric fit. The asymptotic theory developed shows validity of the proposed bootstrap procedure for a large class of periodogram statistics. For important classes of stochastic processes, validity of the new procedure is also established for periodogram statistics not captured by existing frequency domain bootstrap methods based on independent periodogram replicates.