GSBB and extension of MBB for periodic characteristics of PC time series

Anna E. Dudek (1)

1 AGH UST - AGH University of Science and Technology [Krakow, PL]

This research is dedicated to the study of periodic characteristics of periodically correlated time series such as seasonal means, seasonal variances and autocovariance functions. Two bootstrap methods are used: the extension of the usual Moving Block Bootstrap (MBB) and the Generalized Seasonal Block Bootstrap (GSBB). The first approach is proposed, because the usual MBB does not preserve periodic structure contained in the data and cannot be applied for the considered problems. For the aforementioned periodic characteristics the bootstrap estimators are introduced. Consistency of the extended MBB in all cases is obtained. Moreover, the GSBB consistency results for seasonal variances and autocovariance function are presented. Additionally , the bootstrap consistency of both considered techniques for smooth functions of the parameters of interest is obtained. Finally, the simultaneous bootstrap confidence intervals are constructed. A simulation study to compare their actual coverage probabilities for circular versions of the GSBB and the extension of the MBB is provided. A real data example is presented.

Mots clés: Periodically correlated time series; consistency; seasonal means; seasonal variances; autocovariance function

Domaines: Théorie [stat.TH]

Anna E. Dudek. GSBB and extension of MBB for periodic characteristics of PC time series. 2016. ⟨hal-01305810v1⟩