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 .

chart and its predecessors, and the relations among the curves and their significance are comparable with those found in the study of similar index charts extending back to I875. Such changes as have been made in the present revision are directed toward improvement in the accuracy and clarity of the picture given by the three curves. These changes, like those in earlier revisions, have been intended, not to abandon in whole or in part, but to reinforce, the fundamental principle of the chart.'

T HIS article presents a revision of our weekly and monthly series for bank debits outside New York City, I9g9 to date. The revised series have been adjusted for seasonal influences, but the problem of the determination and elimination of secular trend has been reserved for consideration in a later article.' The monthly series corrected for seasonal variation, I9I9-3 i,is given in Table i and Chart i; the corresponding weekly series, in Chart 2.

THE present study is a continuation of that described in a preceding article.' The object of this earlier investigation was to obtain for as long a period as possible prior to the outbreak of the World War an index of business activity as indicated by the fluctuations in a monthly series of aggregate bank clearings based upon a representative group of cities.2 The first installment of the present article contains certain supplementary discussion regarding this aggregate clearings series; the second installment will deal with the analysis of monthly data for eighteen individual cities.

T HE object of this study was to obtain for the United States, for as long a period as possible prior to the outbreak of the World War, a continuous monthly index of business activity as indicated by the fluctuations of bank clearings. In the construction of this index two steps were involved: first, monthly aggregate clearings were secured for a representative group of cities; and second, these monthly aggregates were corrected for long-time trend and seasonal variation, in order that the fluctuations significant of cyclical changes in business activity might be clearly revealed. The results of this study are presented graphically in the two charts appearing as an insert placed opposite this page. Chart i shows monthly aggregate clearings for a group of 7 selected cities, I875-I9I4, together with lines of trend. Chart 2 compares the monthly adjusted relatives of the series of aggregate clearings, corrected for secular trend and seasonal variation, with adjusted relatives for pig-iron production, another series held to be indicative of business activity.'

M ONTHLY index numbers of industrial stock prices for the period 1902-2I, computed by averaging the quotations for the common and the preferred shares of twenty manufacturing companies, are presented graphically in Chart I.' The two series of common and preferred stock indices exhibit marked cyclical fluctuations. These series agree in their indication of the dates at which the important upward and downward swings began, but as might be expected, the common stock index fluctuates much more violently than does the preferred. Looking at the curves of Chart I, we see that during the year 1902 the trend of the common stock index was slightly upward, while that of the preferred stock index was practically horizontal. Early in I903 both indices began a downward movement which lasted for about ten months. There was little recovery until the middle of the following year. Beginning with July I904 a sharp upward movement took place, reaching its highest point in January i906. There then followed in succession the bear market of i906-07 and the bull market of i908-09. Stock prices again declined in i9i0 and i9ii, but did not reach nearly so low a level as they had at the end of the two preceding slumps. The period I9I2-I4 was one in which fluctuations in security prices were much less violent than during the decade preceding; there was slight recovery in I9I2, followed by moderate decline during the two following years. The most noticeable feature of the period I9I5-i8 is the divergence which took place between the movements of the common and the preferred stock indices. During the war years the increased earning power of various industrial corporations reflected itself in the quotations of the common shares, and the common stock index rose until it reached figures considerably above the average for I902-I4; the preferred stocks, except for the relatively small number whose dividend-paying records had been poor during the pre-war period, benefited very much less from the increase of profits, and their prices, on the whole, showed comparatively little change from the pre-war level. Examining in greater detail the movements of the indices through the war period, we see that the year II4 closed with prices at a low level. During the first ten months of I9I5 both series showed a decided upward trend, but weakness then developed in the common stocks, while the preferred stock index moved horizontally. This continued until September i9i6, when both indices began a rapid advance. The recovery was short-lived, however, and prices fell throughout I917. From the end of I9I7 until the signing of the armistice the indices rose steadily.