Journal
JOURNAL OF NONPARAMETRIC STATISTICS
Volume 30, Issue 1, Pages 87-124Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/10485252.2017.1404060
Keywords
Periodically correlated time series; consistency; seasonal means; seasonal variances; periodic autocovariance function
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Funding
- European Union under the Marie Sklodowska-Curie [655394]
- Marie Curie Actions (MSCA) [655394] Funding Source: Marie Curie Actions (MSCA)
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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 Generalised Seasonal Block Bootstrap (GSBB). The first approach is proposed, because the usual Moving Block Bootstrap 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.
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