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APPLYING BUCKET RANDOM PERMUTATIONS TO STATIONARY SEQUENCES WITH LONG-RANGE DEPENDENCE

YINGCHUN ZHOU

Department of Mathematics, Boston University, 111 Cummington St., Boston, MA 02215, USA

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and

MURAD S. TAQQU

Department of Mathematics, Boston University, 111 Cummington St., Boston, MA 02215, USA

Corresponding author.

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https://doi.org/10.1142/S0218348X07003526Cited by:2 (Source: Crossref)

Abstract

Bucket random permutations (shuffling) are used to modify the dependence structure of a time series, and this may destroy long-range dependence, when it is present. Three types of bucket permutations are considered here: external, internal and two-level permutations. It is commonly believed that (1) an external random permutation destroys the long-range dependence and keeps the short-range dependence, (2) an internal permutation destroys the short-range dependence and keeps the long-range dependence, and (3) a two-level permutation distorts the medium-range dependence while keeping both the long-range and short-range dependence. This paper provides a theoretical basis for investigating these claims. It extends the study started in Ref. 1 and analyze the effects that these random permutations have on a long-range dependent finite variance stationary sequence both in the time domain and in the frequency domain.

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