Gerhard Tintner, Book Review: The Analysis of Economic Time Series (1942)

Gerhard Tintner’s review of Harold T. Davis’s The Analysis of Economic Time Series (1941) presents the book as both a synthesis of a difficult statistical field and a source of original mathematical contributions. Its organizing concern is the intellectual cost of specialization: developments in economic statistics may remain unfamiliar to mathematicians even when they bear directly on problems elsewhere in science. Tintner opens with this diagnosis:

It is unfortunate and a sign of the extreme specialization of science and the scientists that many advances made in related fields are ignored or neglected by the mathematicians.

He immediately qualifies the criticism by acknowledging that no individual can follow the expanding literature of every science employing mathematics. Davis’s achievement is therefore not simply comprehensiveness but mediation: assembling and lucidly interpreting scattered research so that readers can recognize connections with their own work. Tintner expects the book to influence time-series analysis and stimulate researchers concerned with apparently unrelated questions. His review follows its twelve chapters, distinguishing established techniques from new results and indicating which sections will matter most to statisticians, mathematicians, and economists.

The historical first chapter supplies an entry into the large volume. Tintner recommends its sixty pages as a means of surveying the field and selecting material without first mastering the entire book. His assessment of the second chapter is more discriminating: the treatment of harmonic analysis, understood as the representation of empirical observations by Fourier series, adds relatively little to classical accounts. Its originality lies instead in connecting harmonic analysis and decomposition by orthogonal functions with multiple correlation. This distinction establishes a recurring evaluative principle: the book is valuable both for clear exposition and for specific extensions of existing methods, but these merits are not identical.

Serial correlation receives particularly strong praise. Tintner explains it through leads and lags among correlated variables, with autocorrelation as the case in which observations within one series correlate with one another. Davis reproduces much of Norbert Wiener’s work while adding theorems and calculation techniques; continuous spectra and random variation also enter the discussion. The application of lag correlation to supply and demand culminates in the cobweb theorem. Here mathematical analysis and economic interpretation are closely connected: temporal dependence matters not merely as a technical complication but as a feature of the processes economists seek to explain.

The chapter on random series broadens the relevance beyond economic statistics. Tintner notes connections with fundamental assumptions of probability, including von Mises’s frequency definition, and describes the generalization of Yule’s theory through the autocorrelation function. Accumulated random series, moving averages, and the theory of sequences and reversals receive attention before an application to stock-market behavior. These topics lead into a central inferential difficulty in the following chapter:

It is well known to the economic statistician that additional observations within the same time interval do not in general add materially to our information about economic phenomena we are studying with the help of statistical methods.

Tintner contrasts this practical recognition with the misleading increase in apparent information produced by an uncritical application of Fisherian degrees of freedom. Davis approaches the issue through inverse probability and Bayes’ theorem, examining significance tests in harmonic analysis and questions in factor analysis before proposing his method of elementary energies. The review praises the ingenuity of this proposal without treating the underlying difficulty as definitively resolved.

The subsequent chapters move from dependence and inference to trends and periodicity. Tintner identifies secular trend with non-periodic movement and outlines treatments of polynomial residuals, seasonal adjustment, and successive finite differences. Logistic fitting receives special attention because its mathematical difficulty accompanies substantial importance for population and related social statistics. Periodogram analysis then provides a technique for seeking hidden periodicities, illustrated through economic observations, sunspot numbers, and galvanometer series. Tintner values this chapter chiefly as a clear presentation of the method.

Economic cycles bring these statistical techniques into contact with explanatory theory. Tintner calls the irregular recurrence of booms and depressions a largely unsolved problem. Davis classifies business-cycle theories, discusses mathematical accounts by Evans, Roos, Frisch, Tinbergen, and Kalecki, and considers statistical hysteresis. His original crisis theory uses a form of resonance explanation. The following chapters turn to wealth and income distributions—including a proposed alternative to Pareto’s function—and dynamic trends viewed through the equation of exchange. Tintner regards these sections as more specifically economic, with the latter less relevant to non-economists.

Forecasting returns the review to the limits of statistical knowledge. After mentioning Henry Schultz’s work on forecast error, Tintner summarizes Davis’s contribution:

Then it presents Professor Davis' own contribution which essentially assumes that it is not possible to forecast in the future beyond a range equivalent to the range of the available data.

Moving periodogram analysis and probable error bands accompany this restriction. Tintner presents forecasting, especially of stock prices, as a difficult problem approached courageously, not as an assured predictive achievement. The final chapter interprets and critiques the preceding material, particularly in relation to business cycles, and offers an economic interpretation of history alongside mathematical-economic analogies.

Tintner’s conclusion returns to the review’s opening concern with communication across disciplines:

This book should prove very useful to the statistician as a handbook.

Its usefulness extends beyond professional economic research. Statisticians gain procedures and stimulation; pure mathematicians gain a survey and encounter unresolved problems, especially in serial correlation and periodogram analysis. Tintner’s central judgment is that Davis has made a dispersed field accessible while preserving its mathematical difficulty. The review’s enthusiastic recommendation rests on readable synthesis, original contributions, and the prospect of further inquiry rather than on a claim that economic time series have yielded their remaining secrets.