TY - JOUR

T1 - Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter

AU - Lieberman, Offer

AU - Phillips, Peter C.B.

PY - 2004/6

Y1 - 2004/6

N2 - 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 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.

AB - 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 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.

UR - http://www.scopus.com/inward/record.url?scp=2542592512&partnerID=8YFLogxK

U2 - 10.1017/S0266466604203024

DO - 10.1017/S0266466604203024

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AN - SCOPUS:2542592512

SN - 0266-4666

VL - 20

SP - 464

EP - 484

JO - Econometric Theory

JF - Econometric Theory

IS - 3

ER -