Gerhard Tintner: Review of Contributions to the Study of Oscillatory Time-Series (1947)

Gerhard Tintner’s review of M. G. Kendall’s Contributions to the Study of Oscillatory Time-Series evaluates a methodological study whose importance lies in exposing the difficulties of inferring economic structure from observed fluctuations. Reviewing Kendall’s 1946 book, Tintner begins with strong praise, then moves through its analytical methods, their disappointing performance on constructed data, and the implications for economic policy. His central judgment combines appreciation of Kendall’s contribution with caution about what statistical analysis can establish.

This is a most valuable contribution to the difficult subject of time series, which is so important for economic statistics.

Kendall extends his earlier studies by examining both empirical economic series and artificial oscillatory series generated by a second-degree difference equation containing a random term. Constructed examples provide a crucial test: the mathematical mechanism is specified, so the performance of analytical methods can be assessed against a known model rather than judged solely by their apparent fit to economic observations.

Tintner describes four approaches: correlograms, periodograms, the variate difference method, and analysis of runs and sequences. Correlograms plot correlations between a series and its lagged values. Periodograms examine amplitudes under an assumption of strictly periodic fluctuations, seeking hidden periodicities; an appendix supplies tables for harmonic analysis. The variate difference method examines the variances of successive difference series. Kendall establishes their close connection with serial correlation coefficients and supplies new formulas for converting one into the other. These advances nevertheless encounter a substantial empirical obstacle.

Even for long artificial series, the empirical results fail to conform even approximately to the theory.

The failure is especially consequential because it occurs in constructed series, where uncertainty about the generating mechanism has been removed. As Tintner presents it, Kendall consequently places greater confidence in runs and sequences, approaches related to work by Wallis and Moore and by Wald and Wulfowitz. His formula for the mean distance between peaks fits the artificial data remarkably well. Tintner nevertheless qualifies this success: the distributions of runs and intervals become complicated, and the book supplies no complete theory.

It is also to be feared that such "nonparametric" methods discard a good deal of the information available in the series.

This reservation prevents the review from treating a promising alternative as a settled solution. Agreement between a particular formula and artificial observations does not establish the general adequacy of the method, especially if the procedure sacrifices information contained in the series.

Tintner concludes by drawing out the broader problem: even fairly long constructed series may not allow statistical criteria to discriminate effectively among competing mathematical models. For economic research, this limits the ability to estimate the structure of the underlying system. Invoking Haavelmo, Tintner stresses that knowledge of this structure is essential to many questions of economic policy. The review’s lasting emphasis is therefore on the gap between analyzing fluctuations and reliably identifying the mechanisms that produce them. Kendall’s contribution makes that gap more visible without claiming to close it.