A complete asymptotic series for the autocovariance function of a long memory processOffer Lieberman and Peter C. B. Phillips () Journal of Econometrics, 2008, vol. 147, issue 1, pages 99-103 Abstract: An infinite-order asymptotic expansion is given for the autocovariance function of a general stationary long-memory process with memory parameter d[set membership, variant](-1/2,1/2). The class of spectral densities considered includes as a special case the stationary and invertible ARFIMA(p,d,q) model. The leading term of the expansion is of the order O(1/k1-2d), where k is the autocovariance order, consistent with the well known power law decay for such processes, and is shown to be accurate to an error of O(1/k3-2d). The derivation uses Erdélyi's [Erdélyi, A., 1956. Asymptotic Expansions. Dover Publications, Inc, New York] expansion for Fourier-type integrals when there are critical points at the boundaries of the range of integration - here the frequencies {0,2[pi]}. Numerical evaluations show that the expansion is accurate even for small k in cases where the autocovariance sequence decays monotonically, and in other cases for moderate to large k. The approximations are easy to compute across a variety of parameter values and models. Keywords: Autocovariance; Asymptotic; expansion; Critical; point; Fourier; integral; Long; memory (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: http://EconPapers.repec.org/RePEc:eee:econom:v:147:y:2008:i:1:p:99-103 Access Statistics for this article Journal of Econometrics is edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao, P. M. Robinson and A. Zellner More articles in Journal of Econometrics from Elsevier |
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