Abstract

Long range dependence (LRD) or long memory, initially observed in data analysis in hydrology, is established in diverse fields, for example in financial economics, networks traffic, psychology, cardiology, etc. The presence of long memory in a stochastic process has important consequences in statistical inferences such is a slower rate of decaying of the variance of the sample mean than the typical rate under short dependence. The block bootstrap has been largely developed for weakly dependent time series. Much of research has focused on the large properties of block bootstrap inference about sample means. The block bootstrap for time series consists in randomly resampling blocks of consecutive values of the given data and aligning these blocks into a bootstrap sample. In this paper, we consider a bootstrap technique, which uses blocks composed of cycles, to estimate the variance of the sample mean. The blocks are compounded by a fix number of cycles. The total number of cycles and their lengths are random. The finite sample properties of the method are investigated by means of Monte Carlo experiments and the results indicate that it can be used as an alternative to other block bootstrap methods.

Keywords

References

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