Semi-parametric estimation of long-range dependence index in infinite variance time series

Liang Peng

Statistics & Probability Letters, 2001, vol. 51, issue 2, 101-109

Abstract: Suppose our data {Xn} come from the model Xt=[summation operator]j=0[infinity]cjZt-j, where {Zn} are i.i.d. with a symmetric distribution function which lies in the domain of normal attraction of a stable law with index [alpha][set membership, variant](1,2). Further we assume that cj=jd-1L(j), where parameter d[set membership, variant](0,1-1/[alpha]) and L is a normalized slowly varying function. Then the above model exhibits two features: long-range dependence and infinite variance. In this paper we show that the semi-parametric estimator for the long-range dependence index d used by Robinson (Ann. Statist. 22 (1) (1994) 515-539) is still consistent for the above semi-parametric model.

Keywords: Long-range; dependence; Stable; law; Semi-parametric; frequency; domain; estimation (search for similar items in EconPapers)
Date: 2001
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