[Statlist] Research Seminar in Statistics *FRIDAY 27 APRIL 2018* GSEM, University of Geneva

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Dear All,

We are pleased to invite you to our next Research Seminar.

Looking forward to seeing you

Organizers :                                                                                   
E. Cantoni - S. Engelke - D. La Vecchia - E. Ronchetti
S. Sperlich - F. Trojani - M.-P. Victoria-Feser

FRIDAY 27 APRIL 2018 at 11:15am, Uni-Mail M 5220

Frequency Domain Bootstrap for Time Series
Efstathios PAPARODITIS - University of Cyprus

ABSTRACT:
We review some developments in bootstrapping time series in the frequency domain. We first discuss some existing frequency domain methods for bootstrapping the periodogram of a time series like the multiplicative periodogram bootstrap, the local periodogram bootstrap, the autoregressive aided periodogram bootstrap and the hybrid wild periodogram bootstrap. We discuss the capabilities of these methods to approximate the distribution of some statistics of interest like spectral means and ratio statistics. We then show that these bootstrap approaches have a limited range. Essentially, these procedures cover the case of linear time series with independent innovations, and some even require the time series to be Gaussian. We then propose a new, hybrid bootstrap method in the frequency domain which is consistent for a much wider range of stationary processes. The method uses existing approaches to replicate the dominant part of the distribution of interest and introduces a new concept of convolved periodograms of subsamples to correct for those aspects that cannot be mimicked by classical procedures. We establish asymptotic validity of the new hybrid bootstrap procedure for general class of stationary time series, ranging clearly beyond linear processes, and for general spectral means and ratio statistics. Some simulations illustrate the finite sample performance of the new frequency domain bootstrap procedure.


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