Title: EstimatedWold Representation and Spectral Density-Driven Bootstrap for Time Series,
Abstract: The second-order dependence structure of purely nondeterministic stationary
process is described by the coefficients of the famous Wold representation.
These coefficients can be obtained by factorizing the spectral density of the
process. This relation together with some spectral density estimator is used in
order to obtain consistent estimators of these coefficients. A spectral
density-driven bootstrap for time series is then developed which uses the
entire sequence of estimated MA coefficients together with appropriately
generated pseudo innovations in order to obtain a bootstrap pseudo time series.
It is shown that if the underlying process is linear and if the pseudo
innovations are generated by means of an i.i.d. wild bootstrap which mimics, to
the necessary extent, the moment structure of the true innovations, this
bootstrap proposal asymptotically works for a wide range of statistics. The
relations of the proposed bootstrap procedure to some other bootstrap
procedures, including the autoregressive-sieve bootstrap, are discussed. It is
shown that the latter is a special case of the spectral density-driven
bootstrap, if a parametric autoregressive spectral density estimator is used.
Simulations investigate the performance of the new bootstrap procedure in
finite sample situations. Furthermore, a real-life data example is presented.