The Problem of Secular Trend - Frickey, Edwin (The Review of Economics and Statistics, 1934)
THIS article will treat the logical problem of the significance of trend-cycle separation in the analysis of time series, and also the related practical problem of choosing the best secular trend representation for a particular economic series. The article will with a discussion of the various points of view which have been held regarding the meaning of secular trend. I. A problem in mathemcatical curve fitting. It might be urged that in establishing a representation for secular trend, closeness of of the curve to the data should be the criterion, and mathematical measures of of fit might be set up, analogous to those employed for frequency series. A fundamental difficulty, however, immediately appears. In applying this principle to secular trends, we must choose a curve which reproduces the underlying movement of the data without bending or twisting, itself so as to conform to the extreme sinuosities, and which at the same time gives a good 'fit' as judged by some arbitrary criterion say, the mean square error.' These two requirements, however, are mutually contradictory,2 and evidently exercise of arbitrary judgment is required in effecting a compromise between them. In a word, our difficulty arises from the fact that we wish to represent not the series itself, but the secular trend of the series, and we are consequently unable to place sole reliance on a mathematical test for goodness of fit. Additional criteria are required. 2. A problem in statistical description. The problem of secular trend might be thought of as a problem in statistical description. Just as we describe the essential characteristics of a fre, quency series by the citation of averages, standard deviations, and measures of skewness, so we might describe the general tendencies shown by a time series through the computation of a line of secular trend. The secular trend has in fact often been defined in some such language as the following: the gradual and persistent movement of the series over a period of time which, contrasted with the short run fluctuations of the series, is long. In fitting the trend line which is designed to furnish a statistical description of the fundamental movements of a particular time series, he decisions as to type of curve and trend interval are by no means matters of indifference. In particular, with reference to the trend interval it is patently inappropriate to combine segments from time periods which are clearly non-homogeneous as would be the case, for example, if the years 1910-22 were selected for a commodity price series. Furthermore, if intervals for trend fitting are chosen indiscriminately, the calculated line is likely to be distorted by the influence of the cyclical movements at the beginning and end of the computation period.3 It is clear, then, that .even though we may fully accept the view that the problem of secular trend is one of statistical description, we have by no means reduced the problem to a mechanical basis, nor have we done away with the necessity for careful examination of the characteristics, and in particular the economic characteristics, of the original data. With respect to the usefulness and validity of the concept of secular trend as a statistical description, there is possibility for contrary opinions. On the one hand, it may be asserted that such a statistical description can have little or no value unless the calculations are preceded by an extensive causal analysis of the forces behind the movements of the series such analysis to be obtained through a theoretical examination of the causal forces in question, or through historical investigation, or both; and still further, that in the absence of an exhaustive analysis of this sort, the determination and representation of secular movements should not be undertaken. The opposing opinion is that until such time as our knowledge regarding economic causation shall be greatly increased, there will still be room for 1Henry Schultz, Statistical Laws of Demand and Supply (Chicago, I928), p. 47. 2 On the one hand we can obtain the curve which actually goes through the points here the sum of the squares of the errors is zero, but the curve is composed of perturbations or sinuosities. On the other hand we can obtain a perfectly smooth curve ... and we obtain a large mean square error.E. C. Rhodes, Smoothing, Tracts for Computers, No. VI (London, I92I), pp. 43-44. 3 The commonly quoted statement to the effect. that in the fitting of a straight-line trend, the interval should begin and end in the same cyclical phase is inadequate. For a precise statement of the criteria, see W. L. Crum. and A. C. Patton, Economic Statistics (Chicago and New York, I925),. p. 3II .