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2015-10-27 Nonlinear Seminar

Elżbieta Gajecka
Resampling methods in the time domain for time series with periodic and almost periodic structure.

(The seminar will be held in room B3-38)

Statistical reasoning, in the case of time series, based on asymptotic distributions cannot always be a basis for effective statistical procedures. However unknown distributions of estimators or statistics can be approximated by the so-called resampling procedures. The idea of resampling methods is obtaining replications of the estimator and calculating the empirical distribution from those replications. The main question, to be answered, is whether this empirical distribution, called the resampling distribution, is close to the real distribution.
Intense research is being conducted towards resampling methods in nonstationary time series, in particular series with periodic and almost periodic structure. During this seminar various methods of resampling, especially subsampling, will be shown. The advantage of subsampling is its insensitivity to the shape of the asymptotic distribution. We will also show conditions of compatibility of resampling methods in the domain of time for $$ \alpha $$-mixing or weakly dependent time series with periodic or almost periodic structure. Especially weak dependency gives new tools to analyse statistical procedures for very general data generating time series, together with periodic series with long memory and heavy tails. An example of a periodic model with heavy tails and long memory will be shown.