Subsampling for heavy tailed, nonstationary and weakly dependent time series

Abstract

We present new results on estimation of the periodic mean function of the periodically correlated time series that exhibits heavy tails and long memory under a weak dependence condition. In our model that is a generalization of the work of McElroy and Politis [35, 42] we show that the estimator of the periodic mean function has an asymptotic distribution that depends on the degree of heavy tails and the degree of the long memory. Such an asymptotic distribution clearly poses a problem while trying to build the confidence intervals. Thus the main point of this research is to establish the consistency of one of the resampling methods - the subsampling procedure - in the considered model. We obtain such consistency under relatively mild conditions on time series at hand. The selection of the block length plays an important role in the resmapling methodology. In the article we discuss as well one of the possible ways of selection the length the subsampling window. We illustrate our results with simulated data as well as with real data set corresponding to Nord Spool data. For such data we consider practical issues of constructing the confidence band for the periodic mean function and the choice of the subsampling window.