Title

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

Document Type

Discussion Paper

Publication Date

7-1-2001

CFDP Number

1308

CFDP Pages

14

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/ π 2 ). 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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