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




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.

Suggested Citation

  • Offer Lieberman & Peter C.B. Phillips, 2001. "Second Order Expansions for the Distribution of the Maximum Likelihood Estimator of the Fractional Difference Parameter," Cowles Foundation Discussion Papers 1308, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1308

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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 463-485, March.
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    More about this item


    ARFIMA; Edgeworth expansion; fractional differencing; pivotal statistic;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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