Title: Frequency domain local bootstrap in long memory time series
Authors: Josu Arteche - University of the Basque Country UPV/EHU (Spain) [presenting]
Abstract: Bootstrapping time series requires dealing with the serial dependence existing in the sample. In the time domain, this task has usually been accomplished by the sieve and the block bootstraps, whose purpose is to resample among approximately independent quantities finally. Frequency domain bootstrap techniques, basically based on transforming time dependence into heteroscedasticity, are less popular but they provide reliable approximations of the distribution of some statistics of weakly dependent series. However, its validity in long memory series has not been analysed yet. A Frequency Domain Local Bootstrap (FDLB) is proposed based on resampling a locally Studentised version of the periodogram in a neighbourhood of the frequency of interest. We analyse the similarities of the distribution of the periodogram and the FDLB distribution in stationary and non-stationary long memory series. A bound of the Mallows distance between the distributions of the original and bootstrap periodograms is offered. The bound is used to justify the use of this strategy for some statistics such as the weighted periodogram or the Local Whittle (LW) estimator. Finally, the finite sample behaviour of the FDLB in the LW estimator is analysed in a Monte Carlo, comparing its performance with rival alternatives.