Estimating the differencing parameter via the partial autocorrelation function

This paper provides an explanation for the puzzling phenomenon in Tieslau ct al. (1996, Journal of Econometrics 71, 249-264) that a substantial efficiency loss occurs if low-order autocorrelations are omitted when estimating the differencing parameter, d. This is because for all it strictly bigger than I,the nth-order autocorrelation function does not depend uniquely on the differencing parameter. We construct a new estimator for the differencing parameter based on the partial autocorrelation function. Comparisons of the asymptotic and finite-sample variance of our estimator and those of TSB are made. A substantial efficiency gain is achieved by our estimator as compared to TSB's. (C) 2000 Elsevier Science S.A. All lights reserved. JEL classification: C22.