The Annals of Statistics, 2006, Vol. 34, No. 2, 1045–1047. DOI: 10.1214/009053606000000182. © Institute of Mathematical Statistics, 2006. A correction is provided for the paper "Efficient parameter estimation for self-similar processes" by Rainer Dahlhaus (1989). The original paper claimed asymptotic normality and efficiency of the Gaussian maximum likelihood estimator (MLE) for long-range dependent processes. However, condition (A9) in the paper ruled out such processes. This condition was relaxed to (A9'), which allows for long-range dependent processes. The results of the paper follow under this weaker condition. The key issue was the proof of consistency for the MLE and the relation on page 1756, line 7 of the original paper. This follows from the equicontinuity in probability of the quadratic form $ Z_{N}^{(0)}(\theta) $. A proposition is stated that under assumptions (A0)–(A8) and (A9'), $ Z_{N}^{(0)}(\theta) $ is equicontinuous in probability. The proof of this proposition follows the lines of the proof of Theorem 6.1 in the original paper. The only additional argument needed is the proof of $ |\mathbf{E}S^{k}| \leq k!(2C)^k $ for k=1, which is quite technical and can be found in the extended correction note [2]. With this result, the following changes have to be made in the original paper: (1) Page 1755, line 5 also holds without (A9); (2) Page 1756, line 7 follows from the equicontinuity stated above; (3) Lemma 5.5 can be skipped completely. Furthermore, the proof of Lemma 6.2 contains a gap, as the proof of $ |\mathbf{E}S^{k}| \leq k!(2C)^k $ is only given for k>1. The case k=1 is not straightforward and can be obtained by a generalization of Lemma 2.1 of [2] to more functions. An alternative is to use Theorem 5.1 of [1] with the restriction $ p(\beta-\alpha) < \frac{1}{2} $. The author thanks Professor Kung-Sik Chan for pointing out the error and for some discussions, and to Professor Hira Koul and two anonymous referees for several helpful comments.The Annals of Statistics, 2006, Vol. 34, No. 2, 1045–1047. DOI: 10.1214/009053606000000182. © Institute of Mathematical Statistics, 2006. A correction is provided for the paper "Efficient parameter estimation for self-similar processes" by Rainer Dahlhaus (1989). The original paper claimed asymptotic normality and efficiency of the Gaussian maximum likelihood estimator (MLE) for long-range dependent processes. However, condition (A9) in the paper ruled out such processes. This condition was relaxed to (A9'), which allows for long-range dependent processes. The results of the paper follow under this weaker condition. The key issue was the proof of consistency for the MLE and the relation on page 1756, line 7 of the original paper. This follows from the equicontinuity in probability of the quadratic form $ Z_{N}^{(0)}(\theta) $. A proposition is stated that under assumptions (A0)–(A8) and (A9'), $ Z_{N}^{(0)}(\theta) $ is equicontinuous in probability. The proof of this proposition follows the lines of the proof of Theorem 6.1 in the original paper. The only additional argument needed is the proof of $ |\mathbf{E}S^{k}| \leq k!(2C)^k $ for k=1, which is quite technical and can be found in the extended correction note [2]. With this result, the following changes have to be made in the original paper: (1) Page 1755, line 5 also holds without (A9); (2) Page 1756, line 7 follows from the equicontinuity stated above; (3) Lemma 5.5 can be skipped completely. Furthermore, the proof of Lemma 6.2 contains a gap, as the proof of $ |\mathbf{E}S^{k}| \leq k!(2C)^k $ is only given for k>1. The case k=1 is not straightforward and can be obtained by a generalization of Lemma 2.1 of [2] to more functions. An alternative is to use Theorem 5.1 of [1] with the restriction $ p(\beta-\alpha) < \frac{1}{2} $. The author thanks Professor Kung-Sik Chan for pointing out the error and for some discussions, and to Professor Hira Koul and two anonymous referees for several helpful comments.