TY - JOUR

T1 - Semi-parametric estimation of long-range dependence index in infinite variance time series

AU - Peng, Liang

PY - 2001/1/15

Y1 - 2001/1/15

N2 - Suppose our data {Xn} come from the model Xt=∑j=0∞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 α∈(1,2). Further we assume that cj=jd-1L(j), where parameter d∈(0,1-1/α) 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.

AB - Suppose our data {Xn} come from the model Xt=∑j=0∞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 α∈(1,2). Further we assume that cj=jd-1L(j), where parameter d∈(0,1-1/α) 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.

KW - Long-range dependence

KW - Semi-parametric frequency domain estimation

KW - Stable law

UR - http://www.scopus.com/inward/record.url?scp=0042867409&partnerID=8YFLogxK

U2 - 10.1016/S0167-7152(00)00122-X

DO - 10.1016/S0167-7152(00)00122-X

M3 - Article

SN - 0167-7152

VL - 51

SP - 101

EP - 109

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

IS - 2

ER -