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Gaussian semiparametric estimation of long range dependence

Robinson, Peter (1995) Gaussian semiparametric estimation of long range dependence. Annals of Statistics, 23 (5). pp. 1630-1661. ISSN 0090-5364

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Assuming the model f(A) GA1- 2H, as A -- 0 +, for the spectral densityo f a covariances tationaryp rocess,w e considera n estimateo f H E (0, 1) which maximizes an approximate form of frequency domain Gaussian likelihood, where discrete averaging is carried out over a neighbourhood of zero frequency which degenerates slowly to zero as sample size tends to infinityT. he estimate has several advantages. It is shown to be consistent under mild conditions. Under conditions which are not greatly stronger, it is shown to be asymptotically normal and more efficientt han previous estimates. Gaussianity is nowhere assumed in the asymptotict heory,t he limitingn ormal distributioni s of very simple form, involving a variance which is not dependent on unknown parameters, and the theory covers simultaneously the cases f(A) -x oc, f(A) -+ 0 and f(A) -+ C E (0, oc), as A -* 0. Monte Carlo evidence on finite-sample performance is reported, along with an application to a historical series of minimum levels of the River Nile.

Item Type: Article
Official URL:
Additional Information: © 1995 Institute of Mathematical Statistics
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
Sets: Departments > Economics
Collections > Economists Online
Date Deposited: 27 Apr 2007
Last Modified: 02 May 2012 12:08

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