An estimate of y obtained by applying the method of maximum likelihood under the assumption that ut is normally distributed is consistent and asymptotically normally distributed. The asymptotic standard deviation is given in this note. Although Kendall considers many estimates of the period in his publication, he does not use the maximum-likelihood estimate although it has desirable properties in large samples that several of the other estimates do not have.4 It is interesting to compare the numerical results of using this estimate with those Kendall applies to four artificial series generated by (1), each series with a different pair of coefficients a and j3.5 If the ut (t , 2, . . . , T) are assumed to be normally distributed and if x-, and x0 are assumed to be fixed, the estimate defined by the method of maximum likelihood is obtained by substituting in (2) the estimates of a and ,B found by the method of maximum likelihood under these assumptions [see equations (8)]. H. B. Mann and A. Wald6 have