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

Liang Peng

doi:10.1016/S0167-7152(00)00122-X

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

Liang Peng^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Suppose our data {X_n} come from the model X_t=∑_j=0^∞c_jZ_t-j, where {Z_n} 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 c_j=j^d-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.

Original language	English
Pages (from-to)	101-109
Number of pages	9
Journal	Statistics and Probability Letters
Volume	51
Issue number	2
DOIs	https://doi.org/10.1016/S0167-7152(00)00122-X
Publication status	Published - 15 Jan 2001

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title = "Semi-parametric estimation of long-range dependence index in infinite variance time series",

abstract = "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.",

keywords = "Long-range dependence, Semi-parametric frequency domain estimation, Stable law",

author = "Liang Peng",

year = "2001",

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

AU - Peng, Liang

PY - 2001/1/15

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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 - https://www.scopus.com/pages/publications/0042867409

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 -

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

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