Gerhard Tintner, Time Series: I. General (1968)

Gerhard Tintner’s encyclopedia article surveys the statistical analysis of economic time series, organizing its exposition around trend, oscillatory movements, interdependence, transformations, and stochastic processes. Its central argument is methodological: observations ordered in time cannot safely be analyzed as independent samples, and techniques that simplify temporal dependence are justified only by assumptions about the process generating the data. Economic policy gives these difficulties practical urgency, since business-cycle and development research depend heavily on time-series evidence.

Tintner begins with four obstacles: simultaneity, errors in variables, multicollinearity, and autocorrelation. Economic observations emerge from interconnected relations, some of which may be unidentified; estimating one relation in isolation can therefore yield inconsistent results. Measurement errors compromise the correspondence between theoretical variables and reported observations, while common influences make it difficult to distinguish the independent effects of correlated explanatory variables. Temporal dependence further undermines conventional inference: collecting observations more frequently need not produce a proportionate increase in independent information.

In practice, all four problems occur simultaneously.

This concise warning governs the survey. Methods commonly address one obstacle while assuming the others away, creating a gap between mathematically manageable problems and actual economic evidence. Tintner consequently treats the traditional decomposition into independent trend, cycle, seasonal, and random components as a useful starting point whose assumptions are increasingly inadequate. His preferred conceptual move is toward a unified account:

It would be preferable to avoid these perhaps unrealistic assumptions, instead employing a procedure based upon the premise that a series is generated by a single model capable of producing trends and fluctuations and incorporating random elements.

A stochastic process supplies this framework, but its generality does not itself solve the statistical problem. Useful inference requires restrictions, and mathematical probability has advanced further than statistical methods for observable processes. Throughout the article, Tintner returns to the mismatch between results justified for large samples and the relatively short series available to economists.

The section on trend makes this tension concrete. Trend means the long-term movement of a series’ expectation, although distinguishing it from a long cycle is difficult. Orthogonal polynomials simplify estimation and the selection of polynomial degree, but a close fit to historical observations offers no assurance of reliable extrapolation: polynomials diverge as time advances. Logistic functions provide an upper asymptote, making them attractive for some development problems, though nonlinear estimation introduces difficulties. Tintner compares Hotelling’s differential-equation procedure with his own difference-equation approach, favoring the latter’s compatibility with observations recorded at discrete intervals.

Moving averages relax the requirement that one function describe the entire series by fitting local subsets. Their apparent simplicity nevertheless conceals consequential changes to the evidence:

Caution must be exercised in the use of moving averages, since the application of such averages will introduce autocorrelation into even a pure random series and modify any existing autocorrelation.

Smoothing can also diminish cyclical amplitudes, while observations near the endpoints require special treatment. Where the form of trend is uncertain, rank-based nonparametric tests offer an alternative to specifying a function in advance. Tintner thus distinguishes detecting a trend from estimating its shape.

For oscillatory movements, the article first considers runs tests for departures from randomness, then contrasts periodogram and spectral analysis. Periodogram analysis represents fluctuations through harmonic components but presupposes strict periodicity and disturbances without subsequent effects—assumptions Tintner considers implausible for economic series. Spectral analysis accommodates variability in amplitudes, periods, and phases. Estimating variation over neighborhoods of frequencies, rather than insisting on exact periodic components, offers a statistically more satisfactory treatment of irregular economic fluctuations.

Autocorrelation becomes the organizing problem of the next sections. Tintner reviews tests for dependence, distinguishes circular from noncircular constructions, and explains autoregressive processes and stationarity. Circular procedures can make distributions mathematically tractable, yet connecting the final observation to the first may introduce economically meaningless terms, especially in trending series. Autoregressive models describe dependence more explicitly, but their estimators can remain biased in small samples. Correlation between two autocorrelated series likewise requires attention to the effective information available, rather than simply the recorded number of observations.

The discussion of regression residuals leads from diagnosis to transformation. Autocorrelation can invalidate conventional standard errors even where coefficient estimates remain unbiased. Remedies include adjusting uncertainty estimates, removing trends, and applying autoregressive transformations such as the Cochrane–Orcutt procedure. Each remedy depends on the underlying process; differencing is not a universally legitimate correction. Tintner gives detrending a particularly pointed interpretation:

However, it should be noted that eliminating trends in variables or introducing time as a separate variable in regression studies is really a confession of ignorance that is sometimes unavoidable.

Removing a shift may stabilize an estimated relation without explaining why it changed. This distinction between statistical accommodation and economic explanation gives the survey its critical edge.

The concluding discussion presents explicit stochastic-process modeling as the most promising direction, illustrating estimation with Poisson and autoregressive processes before turning to interconnected systems. Multiple processes reconnect temporal dependence with the opening problem of simultaneity: estimating reduced-form dynamics does not identify structural coefficients without further restrictions. The article’s lasting methodological relevance lies in this insistence that fitting, transforming, and explaining a series are distinct achievements. Its research priority is better small-sample inference for models that respect both economic interdependence and temporal dependence.