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Second Order Expansions for the Distribution of the Maximum Likelihood Estimator of the Fractional Difference Parameter

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Author Info
Offer Lieberman (Technion-Israel Institute of Technology)
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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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/pi2). This paper develops a second order asymptotic expansion to the distribution of this statistic. 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 make significant improvements in accuracy.

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File URL: http://cowles.econ.yale.edu/P/cd/d13a/d1308.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1308.

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Length: 13 pages
Date of creation: Jul 2001
Date of revision:
Handle: RePEc:cwl:cwldpp:1308

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: ARFIMA; Edgeworth expansion; fractional differencing; pivotal statistic;

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

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References listed on IDEAS
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  1. Phillips, Peter C B, 1977. "Approximations to Some Finite Sample Distributions Associated with a First-Order Stochastic Difference Equation," Econometrica, Econometric Society, vol. 45(2), pages 463-85, March. [Downloadable!] (restricted)
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