Title: A frequency domain bootstrap for general stationary processes
Authors: Jens-Peter Kreiss - Technische Universitaet Braunschweig (Germany) [presenting]
Marco Meyer - TU Braunschweig (Germany)
Efstathios Paparoditis - University of Cyprus (Cyprus)
Abstract: Existing frequency domain methods for bootstrapping time series have a limited range. Essentially, existing frequency domain bootstrap procedures cover the case of linear time series with independent innovations, and some even require the time series to be Gaussian. We propose a new frequency domain bootstrap method which is consistent for a much wider range of stationary processes and can be applied to a large class of periodogram-based statistics. It introduces a new concept of convolved periodograms of smaller samples which uses pseudo periodograms of subsamples generated in a way that correctly imitates the weak dependence structure of the periodogram. We show consistency for this procedure for a general class of stationary time series, ranging clearly beyond linear processes, and for general spectral means and ratio statistics. Furthermore, we show how existing bootstrap methods can be corrected using this new approach. The finite sample performance of the new bootstrap procedure is illustrated via simulations.