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Rates of convergence and optimal spectral bandwidth for long range dependence
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  • Published: September 1994

Rates of convergence and optimal spectral bandwidth for long range dependence

  • P. M. Robinson1 

Probability Theory and Related Fields volume 99, pages 443–473 (1994)Cite this article

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Summary

For a realization of lengthn from a covariance stationary discrete time process with spectral density which behaves like λ1−2H as λ→0+ for 1/2<H<1 (apart from a slowly varying factor which may be of unknown form), we consider a discrete average of the periodogram across the frequencies 2πj/n,j=1,..., m, wherem→∞ andm/n→0 asn→∞. We study the rate of convergence of an analogue of the mean squared error of smooth spectral density estimates, and deduce an optimal choice ofm.

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Authors and Affiliations

  1. Department of Economics, London School of Economics, Houghton Street, WC2A 2AE, London, UK

    P. M. Robinson

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  1. P. M. Robinson
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Robinson, P.M. Rates of convergence and optimal spectral bandwidth for long range dependence. Probab. Th. Rel. Fields 99, 443–473 (1994). https://doi.org/10.1007/BF01199901

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  • Received: 02 January 1992

  • Revised: 16 September 1993

  • Issue Date: September 1994

  • DOI: https://doi.org/10.1007/BF01199901

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Mathematics Subject Classification (1991)

  • 60G18
  • 62G07
  • 62M15
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