Statistical Inference, Estimation and Model Building for Stationary Time Series

9.1

As we saw in §

8.3

, Kendall (1945a) expressed frustration at the lack of a sampling theory related to serial correlations when attempting to interpret the correlograms obtained from his experimental series.

The significance of the correlogram is … difficult to discuss in theoretical terms. … (O)ur real problem is to test the significance of a set of values which are, in general, correlated. It is quite possible for a part of the correlogram to be below the significance level and yet to exhibit oscillations which are themselves significant of autoregressive effects. At the present time our judgments of the reality of oscillations in the correlogram must remain on the intuitive plane. (

ibid.

, page 103)

In his discussion of the paper from which this quote is taken, Bartlett actually took Kendall to task for not attempting any form of inference: ‘it might have been useful, and probably not too intractable mathematically, to have evaluated at least the approximate theoretical standard errors for the autocorrelations’ (

ibid.

, page 136). This rebuke may have been a marker for a major development in the sampling theory of serial correlations that was to be published within a year of the appearance of Kendall’s paper.