Gerhard Tintner, The Analysis of Economic Time Series (1940)

Gerhard Tintner’s methodological journal article examines why economic observations ordered through time resist the statistical procedures developed for independent samples. Its central distinction is between identifying random variation and analyzing the systematic movements that matter most to economists. These are different problems, requiring different justifications. Tintner moves from the conditions of statistical inference through methods of decomposing individual series to relationships among several series, concluding with the reciprocal dependence of statistics and economic theory.

The initial difficulty is not merely that economic data are complicated, but that their temporal organization undermines an assumption of ordinary inference:

Items of data which are ordered in time are in general not mutually independent or random in time.

Successive observations may depend on one another, and their variance may change over time. Tintner therefore makes investigation of a series’ random character logically prior to estimation and hypothesis testing. His account of modern statistics emphasizes its ability to distinguish substantive results from chance fluctuations: consistent estimation improves with increasing sample size, while hypothesis testing distinguishes rejecting a true hypothesis from failing to reject a false one. These advances cannot simply be transferred to economic series without examining the conditions that give them probabilistic meaning.

Tintner surveys two approaches to this preliminary problem. The Variate Difference method assumes that finite differencing can eliminate all or part of the systematic component locally; it does not require the entire series to follow a polynomial. His own extension seeks exact significance tests for short series by selecting observations so as to create artificial independence. That solution has a deliberate cost:

Some of the available information is hence lost and the method is not efficient.

The admission identifies a trade-off between valid inference and efficient use of data. The alternative approach, associated with Yule and developed extensively by Wold, investigates serial correlation and connects with differencing and harmonic analysis. Tintner nevertheless regards its practical statistical application as insufficiently developed. Neither approach supplies an uncomplicated route from dependent observations to ordinary inference.

Separating random from nonrandom variation also leaves a second task unresolved: decomposing systematic movement into seasonality, business cycles, trends, and longer waves. Tintner evaluates such procedures through two criteria. First, their assumptions must be intelligible within economics, particularly a theory capable of addressing dynamics and risk. Statistical techniques should accord with their subject matter, just as methods in genetics or physics accord with the theories of those sciences. Second, they must accommodate changing economic relations:

The statistical methods used in dealing with economic series ought to be as flexible as possible.

This requirement grounds his skepticism toward rigid trend formulas and periodogram analysis with fixed periods. He allows qualified exceptions: a logistic trend may suit phenomena connected with population growth, and comparatively stable seasonal movements may permit Fourier analysis. For less stable movements, he favors adaptable procedures, including moving averages of empirically determined length and the approaches of Kuznets, Wald, and the National Bureau. Yet flexibility does not eliminate interpretive uncertainty. Seasonal, cyclical, and trend components may interact, whereas decomposition commonly neglects those relationships. Their separation yields cautious approximations, not demonstrably independent economic mechanisms.

The article’s sharpest argument concerns relationships between series. Removing a trend does not necessarily remove dependence among successive observations; correlation coefficients can consequently remain misleading. Tintner draws a restrictive boundary:

It is my own feeling that the idea of correlation is, by necessity, restricted to the random parts of the series which are investigated.

Correlated random components may admit ordinary statistical treatment, possibly after selecting sufficiently spaced observations. Relationships among systematic components should instead be called “covariation.” A regression fitted to nonrandom series can minimize squared deviations and thus be mathematically optimal without having an inferential interpretation. If its residuals remain patterned through time, conventional significance claims lack the independence on which they depend. Tintner presents this objection categorically, within the statistical framework he is assessing; he leaves the treatment of distributed lags, dimensionality, and stochastic dynamic equations as unfinished problems.

This restriction produces the article’s central tension. The components most accessible to existing probabilistic methods are often economically secondary, while persistent causes appear in precisely the systematic movements those methods cannot adequately handle:

But, in general, the economically important and more significant part of the series is exactly the nonrandom part which is the effect of the more permanent causes in economic life.

Weather-dependent series provide an important exception. Otherwise, Tintner calls for new methods adapted to economic dependence rather than the indiscriminate borrowing of techniques successful elsewhere. The article’s relevance lies in its insistence that a good numerical fit, a plausible economic description, and a warranted probability statement are distinct achievements.

The conclusion preserves an ambitious role for statistics despite these limitations. Where experimental isolation is unavailable and ceteris paribus conditions rarely hold, statistical testing can partially substitute for experiment. But induction requires coherent economic hypotheses, and the methods used to test them must themselves respect economic experience. Tintner thus makes theory both a source of testable propositions and a constraint on statistical construction: empirical rigor depends on explaining what the observations represent before deciding what their calculated relationships establish.