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Rates of convergence and optimal spectral bandwidth for long range dependence (1994)

Robinson, P. M.

Springer

Probability theory and related fields 99 (1994), S. 443-473

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ISSN: 1432-2064

Keywords: 60G18 ; 62G07 ; 62M15

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01199901

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