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

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  • Peng, Liang

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.

Suggested Citation

  • Peng, Liang, 2001. "Semi-parametric estimation of long-range dependence index in infinite variance time series," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 101-109, January.
    • Handle: RePEc:eee:stapro:v:51:y:2001:i:2:p:101-109
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    References listed on IDEAS

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    1. Kokoszka, Piotr S. & Taqqu, Murad S., 1995. "Fractional ARIMA with stable innovations," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 19-47, November.
    2. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    3. Kokoszka, P. & Mikosch, T., 1997. "The integrated periodogram for long-memory processes with finite or infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 66(1), pages 55-78, February.
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