Estimating the differencing parameter via the partial autocorrelation function

This paper provides an explanation for the puzzling phenomenon in Tieslau et 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 n strictly bigger than 1, 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 TSBʹs.