EXPANSIONS FOR THE DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE FRACTIONAL DIFFERENCE PARAMETER
研究了高斯ARFIMA(0,d,0)模型中分数差分参数最大似然估计量的分布，给出了渐近展开式，发现该估计量对d是二阶枢轴的，且展开式能显著改进正态近似的精度。
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/π2). 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.