Title: Estimated Wold representation and spectral density driven bootstrap for time series
Authors: Jonas Krampe - University of Mannheim (Germany) [presenting]
Jens-Peter Kreiss - Technische Universitaet Braunschweig (Germany)
Efstathios Paparoditis - University of Cyprus (Cyprus)
Abstract: For purely nondeterministic stationary processes, the spectral density is factorized to get coefficients of a moving average representation of the process which, appropriately normalized, are identical to those of the Wold representation. This relation together with a spectral density estimator is used to obtain estimators of these coefficients. A moving average bootstrap for time series is then developed which uses the entire sequence of estimated moving average coefficients together with appropriately generated pseudo-innovations to obtain new pseudo-time series. It is shown that if the underlying process is linear and the pseudo-innovations are generated by means of an i.i.d. wild bootstrap which mimics, to the necessary extend, the moment structure of the true innovations, then this bootstrap asymptotically works for a wide range of statistics. The relations of the new bootstrap procedure to the linear process bootstrap and to the autoregressive sieve bootstrap are discussed, with the latter being a special case of the moving average bootstrap, when an autoregressive spectral density estimator is used. Simulations investigate the performance of the new bootstrap procedure in finite samples and a real-life data example is presented.