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Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter

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Lieberman, Offer
Phillips, Peter C.B.

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Abstract

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0,d,0) model is well known to be asymptotically N(0,6 2). This paper develops asymptotic expansions to the distribution of this statistic under the assumption of a known unit variance. The correction term for the density is shown to be independent of d, so that the MLE is second-order pivotal for d. This feature of the MLE is unusual, at least in time series contexts. Simulations show that the normal approximation is poor and that the expansions can make a significant improvement in accuracy provided the correction terms are computed without further asymptotic approximation.This paper was commenced and revised while Lieberman was visiting the Cowles Foundation during 2000 2002. Lieberman thanks the Cowles Foundation for support and hospitality during this visit. Phillips thanks the NSF for support under grants SBR 97-30295 and SES 0092509.

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Publisher Info
Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 20 (2004)
Issue (Month): 03 (June)
Pages: 464-484
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Handle: RePEc:cup:etheor:v:20:y:2004:i:03:p:464-484_20

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  1. Offer Lieberman & Peter C. B. Phillips, 2006. "Refined Inference on Long Memory in Realized Volatility," Cowles Foundation Discussion Papers 1549, Cowles Foundation, Yale University. [Downloadable!]
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  2. D. S. Poskitt, 2006. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Monash Econometrics and Business Statistics Working Papers 12/06, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  3. Offer Lieberman & Peter C.B. Phillips, 2006. "A Complete Asymptotic Series for the Autocovariance Function of a Long Memory Process," Cowles Foundation Discussion Papers 1586, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
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