کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5097107 1376571 2008 5 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A complete asymptotic series for the autocovariance function of a long memory process
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آمار و احتمال
پیش نمایش صفحه اول مقاله
A complete asymptotic series for the autocovariance function of a long memory process
چکیده انگلیسی
An infinite-order asymptotic expansion is given for the autocovariance function of a general stationary long-memory process with memory parameter d∈(−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 {0,2π}. 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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Econometrics - Volume 147, Issue 1, November 2008, Pages 99-103
نویسندگان
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