Block bootstrap for periodic characteristics of periodically correlated time series

Anna E. Dudek (1, 2, 3)

1 Centre de Recherche de Statistiques - Rennes 2
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 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 (EMBB) and the Generalized Seasonal Block Bootstrap (GSBB). The first approach is proposed, because the usual MBB does not preserve the periodic structure contained in the data and cannot be applied for the considered problems. For the aforementioned periodic characteristics the bootstrap estimators are introduced and consistency of the EMBB 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 is provided. A real data example is presented.

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

Domaines: Théorie [stat.TH]

Anna E. Dudek. Block bootstrap for periodic characteristics of periodically correlated time series. Journal of Nonparametric Statistics, 2018, 30 (1), pp.87-124. ⟨10.1080/10485252.2017.1404060⟩. ⟨hal-01305810v3⟩