Séminaire MODAL'X : Anna Dudek (AGH University of Krakow)

Résumé :
Seasonality appears naturally in economics, vibroacoustics, mechanics,
hydrology and many other fields. Periodicity is often present not only
in the mean but also in the covariance function. Thus, to build statistical
models periodically correlated (PC) processes are used. The purpose of
the talk will be to present two block bootstrap methods that can be applied
for periodic time series. These are the Extension of Moving Block Bootstrap
(EMBB) and the Generalized Seasonal Block Bootstrap (GSBB). The GSBB
preserves the periodic structure of the data and in result the consistent
estimators of time and frequency domain parameters of PC time series can
be easily constructed. However, to apply the GSBB one needs to know the
period length. Sometimes it may happen that period length is not known
or considered signal is a composition of two components with
incommensurable periods. In such a case the EMBB can be used.
We discuss the consistency of the GSBB and the EMBB for parameters
associated with PC time series; these are  the overall mean,
seasonal means, the autocovariance function and the Fourier coefficients
of the autocovariance function. Finally, we discuss the problem of choosing
the optimal block length for the both block bootstrap methods.