PROGRAMMEDSELECTIONOF CYCLICAL TURNING POINTSPRINCIPLES OF SELECTING T - PDF document

PROGRAMMEDSELECTIONOF CYCLICAL TURNING POINTSPRINCIPLES OF SELECTING TURNING POINTSFOR THE CYCLICAL ANALYSIS of time series, distinction between dif-ferent segments of cyclical movements is desirable. Such distinctionprovides a framework for orderly description. Also, behavior can beexpected to differ from segment to segment, and it is hoped that thisbehavior is sufficiently homogeneous within segments to permit gener-alized description and explanation. Plausible distinctions exist betweenperiods of cyclically high and cyclically low levels of activity or be-tween periods of cyclical increases and declines. Combination of thesetwo distinctions has led to various schemes of three, four, or even morephases. Characteristically, these schemes identify the neighborhoodsof cyclical peaks and troughs, and partition the upswing and usuallyalso the downswing. This leads to sequences such as recovery—pros-perity—recession——depression; upswing—boom-—downswing-—depres-sion; primary rise—secondary rise—boom-—capital shortage—crisis—recession; or recovery—growth-—contraction. In these sequences, liketerms do not necessarily describe like periods. The segmentation maybe determined on the basis of inflection points of fitted cyclical curves,intersection of trend and cyclical values, maximal changes in cyclicalmovements, attainment of prior peak levels, or by other criteria.Most of these criteria are not specific enough to yield unique statisticalresults. The segmentation tends to vary, for example, with the periodfor which cyclical curves or long-term trends are fitted, and with thechoice of functions for these curves. Also, the statistical determinationof fastest changes leaves much to the discretion of the investigator.Because of all these problems, it has been a widely accepted practiceof the National Bureau of Economic Research to distinguish only two Cyclical Analysis of Time Seriesphases—expansions and contractions—which are delineated by cyclicalturningWhile the restriction to two phases reduces the statisti-cal problem to that of determining cyclical turns—points that can bebetter defined and identified than most others—it does not eliminatethe need for subjective decisions. This need may, however, be furtherreduced by the use of programmed procedures. It is the determina-tion of specific cyclical turning points (peaks and troughs in specifictime series) with which this chapter is concerned. This encompassesan exposition of the principles and problems as well as a discussion ofprogrammed procedures.SELECTING CYCLESChart 1 depicts time series of seasonally adjusted employment andunemployment, showing numerous fluctuations. The first problem isthat of determining which of the fluctuations in these series should berecognized as cyclical (specific cycles). Basically, we are looking forclearly defined swings of the same order of duration as business cycles,that is, for swings that are longer than fifteen months but shorter thantwelve years from trough to trough or from peak to peak. Mostspecific cycles identified by the National Bureau have lasted betweentwo and seven years. We also require the amplitudes of specific cyclesto be larger, on average, than those of irregular fluctuations encoun-tered in the series.2 In most instances, the identification of cycles inemployment and unemployment is simple. The two series show well-defined swings with fairly certain highs and lows, which are indicatedby X's on the chart. Even a casual examination reveals that the ob-served swings are rather regularly related to the expansions and con-tractions in general business activity, which are indicated on the timegrid of the chart.However, a number of problems may arise in conjunction with theidentification and dating of specific cycles. Take, for instance, thequestion of whether or not a particular fluctuation in a time seriesshould be recognized as a specific cycle. Chart 2, panel A, shows theproblem in schematic form. Should the swing a—b—c be regarded asa cycle or as part of a larger expansion a—d? What criteria shouldThe partition of expansions into recovery and growth periods is discussed inChapter 3 (p. 71).2 See Arthur F. Burns and Wesley C. Mitchell, MeasuringBusiness Cycles,New York, NBER, 1946, Part I, Chapter 4. NONAGRICULTURAL EMPLOYMENT AND UNEMPLOYMENT RATE, 1929-65Per cent20Total Unemployment RateMill6050'II'IIIIIIr'IIIIlxiiI'III1929'35'40'45'50'55'60'65Nonagricultural EmploymentOflSIIIIIIIIIIIIIIIIIIIII1111111!40309n1929'35'40'45'50'55'60'65 Cyclical Analysis of Time Seriesguide such a decision? One National Bureau rule is that specific cyclesshould have a duration of at least fifteen months. Another is that theamplitude of a doubtful expansion or contraction should not be ma-terially smaller than that of the smallest clearly recognized cycle inthe series. Chart 1gives a practical illustration of the problem. Theincrease in the unemployment rate in the second half of 1959, whichoccurred in connection with the steel strike, appears as a fluctuationof more than random character. It is not recognized as a specific cyclesince it does not approximate, in duration or amplitude, the lowerlimit of cyclical fluctuations in this series. A similar situation existsaround 1933—34.It is not by chance that the activities here selected, employmentand unemployment, contain clear specific cycles but no example ofextra cycles, that is, of specific cycles in addition to those related tobusiness cycles. This is due to the very broad coverage of the two series,both of which reflect changes in general business activity rather thancircumstances peculiar to an industry or area or activity. However, theoccurrence of extra cycles is far from rare. Many sensitive series showspecific cyclical declines and subsequent recoveries during the years195 1—52 in connection with the Korean War, and many activitiesrelated to the automobile industry show extra cycles during 1954—57.Specific cycles can also be considerably longer than reference cy-cles. This occurs particularly when business cycle contractions are"skipped," as happens frequently in rapidly growing industries, andwhen the business contraction itself is mild. For a schematic illustra-tion, see panel B of Chart 2. Specific cycles can, of course, also beunrelated or only loosely related to business cycles. This is frequentlyfound, for instance, in series describing the harvest of agriculturalcrops, the exports of specialties, or fashion goods. These activities arestrongly influenced by factors other than domestic business conditions.SELECTING PEAKS AND TROUGHSAfter specific cycles have been identified, it is still necessary to pin-point specific peaks and troughs. This may raise a large number ofquestions, some of which have to be answered on the basis of ruleswhich, though occasionally arbitrary, are needed in order to ensureconsistency of treatment. In general, cyclical peaks and troughs areplaced at the highest and lowest points of the cyclical fluctuations.Peaks and troughs alternate; i.e., a peak cannot succeed another peak iiCHART 2PROBLEMS OF TURNING POINT DETERMINATIONAIEutra cyclemeLast of equal.DDouble turns//ER,JR2Step patternsV2IF;Virtual steppatterns withirregularitiesVtJINote: Circles denote specific cycle turning points. Vertical lines stand for alter-nating peaks and troughs in general business activity. Cyclical Analysis of Time Serieswithout an intervening trough. Hence peaks should not be identifiedat the ends of series unless it is clearly possible for the next succeed-ing turn to be a trough; analogous considerations apply to troughs.In case of equal values the rule is to choose the last one as the cyclicalturn, i.e., the month before the reversal of the cyclical process begins.Exceptions to this general rule are necessary when the values in ques-tion are clearly extreme, isolated, and possibly compensated for orsurrounded by other values that deviate in the opposite direction.Panel C of Chart 2 portrays this situation and the appropriate choiceof turn, indicated by a circle. On Chart 1, the unemployment low inFebruary 1960 provides an example from historical experience. Therate in that month is lower than the lowest rate in mid-1959, but theFebruary low is comparatively isolated, and therefore the June 1959position is regarded as the cyclical low point. When random move-ments complicate the determination of specific turns, some guidancecan be obtained through smoothing by moving averages. The inter-mediate output tables and corresponding charts of some seasonal anal-ysis programscan be of great help in deciding doubtful cases, bothwith regard to recognition of cycles and determination of turns. Butthe cycles and their turning points are eventually identified in theseasonally adjusted data, not in the smoothed series.Sometimes a difficulty arises in cases of "double turns," that is,when a series returns to its previous peak or its previous trough levelafter some intermediate fluctuation. The decision in case of doublepeaks or double troughs is, of course, a very important one for timinganalysis, since a minor difference in level and a marginal decision inthe selection of turns can cause relatively large differences in tim-ing and duration measures. The basic rules prescribe that the peakbe the last high month just preceding the month in which the down-ward movement starts. However, if the period between the two peakscontains mainly downward movements and only one or two steep rises,the first high should be chosen. Panel D of Chart 2 depicts this situa-tion as well as the application of the decision rule. The double turnsin the unemployment rate during 1946 and 1958 do not really presenta problem, since the turns to be chosen are obviously those that arelater and higher.There are cases in which, instead of showing clearly defined turns,the series maintains a peak or a trough level for several months in aIntermediate output tables of curves smoothed by a variety of moving aver-ages can be found in the Census and BLS seasonal adjustment programs. 13row. The basic rule is still to regard the last of the equal values asthe turn, since the decisive change of cyclical direction manifests itselfonly after that month. However, if a series forms a definite step pat-tern in which plateaus and changes between plateau levels are com-mon, the search for "turning points" may be inappropriate. In suchinstances it may be desirable to identify the beginnings and ends ofridges (R) and valleys (V), as illustrated in Chart 2, panels E and F.4Some economic time series do not show actual cyclical declines,but do show clear cyclical behavior in terms of accelerations and re-tardations. Time series depicting economic activities with strong growthcharacteristics offer many examples of such behavior. The question ishow such series, as illustrated by panel G of Chart 2, may be sub-jected to cyclical analysis. One possibility is to adjust them for trend,that is, to fit a trend line to the observations and to analyze the devia-tions from these trends. However, the trend will vary with the choiceof the trend function, the criterion of best fit, and the time periodcovered. Any of these alternatives, and therefore also the incorpora-tion of newly available information, influences the computed trendand hence the deviations and the cyclical measures. It may thereforebe preferable to use a different approach and to analyze first differ-ences or the month-to-month percentage change of the original data.When the original series undergoes cyclically regular accelerations andretardations, these derived data will show analyzable cycles.Each solution, however, produces its own problems. First, absolutedifferences or rates of change are apt to show large random move-ments relative to the size of their cyclical component. This makes itdifficult to date cyclical peaks and troughs. Second, the cyclical timingof these near derivatives differs systematically from that of the originalseries. First differences experience their highs at the points of thegreatest absolute increase of the parent series—that is, whenever theexpansion process is most rapid. The turns of these derivatives should,perhaps, be related to the points of maximum rate of expansion orcontraction in the economy as a whole. Alternatively, locations corre-sponding to turning points in the original series could be determinedby identifying shifts in the levels of first differences or rates of change.4Forexamples of dating steps rather than turning points, see Gerhard Bry,Wages in Germany, 1871—I 945, Princeton, N.J., Princeton University Press forNBER, 1960, p. 138; Daniel Creamer, Behavior of Wage Rates during BusinessCycles, New York, NBER, 1950, pp. 6 if.;Milton Friedman and Anna J.Schwartz, "Money and Business Cycles," Review of Economics and Statistics,Supplement, February 1963, pp. 35—37. Cyclical Analysis of Time SeriesSuch identification is simple if there are marked shifts, that is, if theoriginal series has clear alternations of fast and slow growth. Identifi-cation of such shifts will be impossible if the growth of the underlyingseries changes gradually, e.g., if the cyclical component of the originalseries is sinusoidal rather than triangular. Economic time series arenot likely to correspond to either extreme. Thus the feasibility of de-fining shifts in the derivatives(as approximations to turns in theoriginal series) is an empirical rather than a theoretical question. Pre-liminary experiments with this approach seem promising. Further tech-nical developments may widen the scope of its application.Turning point determination might, finally, be influenced by theconsideration of factors that lie outside the analyzed series. If oneseries is analyzed at a time, without reference to other activities, rigor-ous application of the standard rules is called for. However, in con-nection with a particular research project, substantive considerationmay be overriding. Take, for example, the industry-by-industry analy-sis of the relation between peaks in hours worked, employment, andproduction. The steel strike at the end of 1959 affected the upperturns of many of these activities drastically. The measures of timingrelations would vary in a haphazard manner if sometimes the pre-strike, and sometimes the poststrike, maxima were selected as peaks.A research worker might thus be justified in basing his comparisonson, say, the poststrike peaks even if on occasion the prestrike maxi-mum was a bit higher.It is true, on the other hand, that such a decision might occasionallyprejudice research results. For example, the arguments which sug-gested the selection of the poststrike peak in hours might also lead tothe selection of the second peak in accession rates, although theserates typically show very early declines occurring shortly after theinitial business recovery. Reasonable decisions on such matters canonly be derived by an iterative process in which the growing knowl-edge of the subject matter is permitted to modify approaches anddecisions.PROBLEMS OF PROGRAMMED SELECTIONGENERAL CONSIDERATIONSThe importance of cyclical turning points for cycle analysis and thecriteria for their selection were discussed above. Some rules were de-A ProgrammedSelection of Turning Points15scribed which aimed at minimizing the role of individual judgment inthe determination; yet in the formulation of these rules and still morein their implementation, individual judgment continues to play animportant role. Determination of turning points can have far-reachingconsequences for analysis; specifically it affects all basic measures ofcyclical durations and amplitudes. Thus itis desirable to free theprocess as far as possible from the uncertainties of varying interpreta-tion and from bias in the implementation of the basic rules. Progresstoward greater independence from personal interpretation could bemade, if it were possible to codify the relevant rules and considera-tions, to reduce the selection to a programmed sequence of steps, andto relegate the process to execution by electronic computer. The pur-pose of the efforts described in the present section is to test the feasi-bility of this approach.The development of a programmed turning point determination isa process which has only recently been initiated. It may involve pro-liferation, tightening, or reformulation of rules, and it may necessitatesome changes in the basic approach. Hence, what we have to reportat this stage is provisional, much as was the case for the early programsfor seasonal adjustment of economic time series. Since it is unlikelythat all contingencies can be covered by any programmed approach,and since certain research objectives may require modification of rules,some overruling of the program will no doubt still be necessary in atyp-ical situations and for special purposes. In such cases, the overrulingshould be explained and justified.ALTERNATIVE APPROACHESThe technique described in this study is an adaptation of the NationalBureau method. It converts this method to a sequence of relativelysimple decision rules by which neighborhoods of turns and potentialturning points are selected and tested for compliance with a number ofconstraints.This obviously is not the only possible approach. One alternative—albeit complex and time consuming—would be the simulation of theprocess of turning point determination as practiced by an experiencedanalyst. The advantage as well as the difficulty of such simulationwould lie in greater freedom when dealing with special circumstances.In such simulation, for example, turns in the neighborhood of strikes Cyclical Analysis of Time Seriesmay more likely be rejected and turns in the neighborhood of businesscycle turns accepted.Another possibility would be to disregard the National Bureaumethod and to formulate a rigorous search-and-test procedure, basedon strictly defined statistical properties of given time series. One sug-gested approach along these lines is based on the assumption thatcyclical expansions and contractions in time series can be distinguishedby the level of their first-order differences. Peaks are located wherepositive first differences change to negative differences, troughs wherethe obverse change occurs. Even cyclical changes in slopes or in ratesof expansion and contraction could be similarly identified, except thathere the "steps" in the first-order differences would not involve achange of sign. The statistical procedure to determine turning pointsand other changes in slope is a segmentation of time series on thebasis of statistically significant steps in the levels of their first-orderdifferences; the steps are selected by minimizing the variances withineach segment.5APPROACH EMPLOYEDThe approach employed here is related to the process of turning pointdetermination practiced by the National Bureau of Economic Research.It roughly parallels the traditional sequence of first identifying majorcyclical swings, then delineating the neighborhoods of their maximaand minima, and finally narrowing the search for turning points tospecific calendar dates. However, at the present time, the programneglects certain elements that are part of the traditional technique anduses some additional measures and rules.The programmed strategy involves, first of all,the derivation ofsome moving averages representing trend and cycle elements only.These relatively smooth curves serve as the basis for determining theexistence of expansions and contractions and for selecting the generalneighborhoods of potential peaks and troughs. Local maxima andThis approach was suggested by Milton Friedman, and a preliminary programwas developed by Charlotte Boschan. It is particularly important in connectionwith the determination of cyclical phases in fast-growing series, as discussed above(see, for example, use Mintz, Dating Postwar Business Cycles: Methods and TheirApplication to Western Germany, 1950—67, New York, NBER, 1970). Otherapproaches, incorporating perhaps some features of spectral analysis (e.g., to testthe existence of cycles of a specified range of durations) are also worthy ofexploration. 17minimaare excluded by postulating a minimum cycle duration; shorterfluctuations are eliminated in such a way that only major peaks andtroughs remain. Next, the neighborhood of potential turns is redefinedby identifying peaks and troughs corresponding to those of the trend-cycle curves on a time series that is only slightly smoothed by a short-term moving average. The objective here is to come closer to theeventual location by excluding the influence of values that may beseveral months removed from the final turns. Once the immediateneighborhood of potential turns is established on this curve, the anal-ysis shifts to the unsmoothed data. The highest (or lowest) originalvalues within a short span of the turns on the smoothed curve arechosen as preliminary turning points. These turns are tested for aminimum cycle duration rule and for compliance with some otherminor constraints; elimination of disqualified fluctuations leads to theselection of final turns.Consideration of this plan of attack makes it clear that numerouschoices must be made in the implementation of the approach. Whattype of moving average, if any, should be chosen to represent trend-cycle elements of what length and using what weights? Should extremeirregular values be excluded in the derivation of these trend-cycle func-tions, and, if so, what are the criteria for exclusion and the rules ofsubstitution? Within what span should a value on the trend-cycle curvebe the highest (or lowest) to be recognized as establishing the neigh-borhood of a potential cyclical turn? Should there be minimum limitsfor the duration of cycles, for the duration of phases, or perhaps forexpansions only? Should minimum durations be the same for expan-sions and contractions, and, if not, how should inversely related activ-ities, such as unemployment, be handled? What should the values ofthese minima be? Should any minimum duration requirements, for fullcycles or cycle phases, be applied to all derived curves, to some ofthem, or only to the unsmoothed data? Can amplitudes be safelyignored or must minimum amplitudes be specified?The variety of possible answers to this sample of queries suggeststhat turning point determination is not simply a process of discovering"true turns." It cannot be regarded as objective in the sense that allreasonable and conscientious investigators would agree on the answers.Only agreement on the application of a specific set of detailed, andsometimes arbitrary, procedural conventions could bring about agree-ment on the choice of turns. Cyclical Analysis of Time SeriesSome of the choices among procedural alternatives can be madeTheion the basis of traditional practices, that is, by decision rules that helpthe leto maintain consistency with existing procedures. Enforcement of aby thfifteen-month minimum duration rule for full cycles is a case in point,in itsIn other instances, one stratagem may be given preference over an-Condother for reasons of simplicity. It would, for instance, complicate mat-ters considerably if the programmed determination of turning pointsworkspecified amplitude minima.6 Hence, the present approach neglects am-plitude considerations, except for those implicit in the various smooth-ing processes. Other questions may have to be answered on purelypragmatic grounds. If the procedure recognizes too many short andBitunshallow fluctuations as cycles, the admission criteria must be tightened.of tuThis can be done in a variety of ways, for instance, by choosing lessandflexible (longer-term or differently weighted) trend-cycle approxima-minoltions, by lengthening the span within which a peak is chosen or bydiscujextending duration minima. In order to choose between these tacticalThe ialternatives, it is necessary to analyze not only the nature of the con-tive atingencies that should be avoided but also the effects of alternativecurvestratagems on the over-all efficiency of the chosen procedure. TheThe Iquestion is whether any proposed alternative improves the process atlarge or only the results for a particular activity. This characterizesandthe approach and the choice between alternative criteria of selectionare uas essentially heuristic.serietIn order to describe the selection process as well as the directionof desirable improvements, the experimental procedure currently inuse wiU be described in some detail and illustrated by the monthlySincebituminous coal production series from 1914 to 1938. The computerthe iioutput of the analysis is presented in the Appendix to this chapter.6Thecomplication would arise from the difficulty of setting adequate stand-ards. Minimum amplitudes should be different for volatile and for stable activities,and thus presumably should be expressed in terms of average cyclical volatilityfor a given activity during reference cycle phases (since the determination ofrspecific cycles now would hinge upon the volatility measure). To apply uniformhigheistandards, these averages should cover the same time periods. Moreover, the mildthe cresponse of a given activity to a mild contraction in general business conditionsfiexiblmay well be cyclically significant, irrespective of contraction amplitudes duringSpencother cycles. This raises the problem of comparison of cyclical amplitudes foreffectany given activity with swings in business conditions at large or in representativeflirnilactivities—certainly no simple matter. Although it may be theoretically and tech-causenically feasible to incorporate explicit amplitude considerations in programmedtimes.turning point selection, such incorporation would complicate the procedures con-procasiderably and perhaps render them impractical.- 19madeThe procedure will then be applied to a group of time series—to wit,helpthe leading, coinciding and lagging business cycle indicators as reportedof aby the Bureau of the Census of the U.S. Department of Commerce,oint.in its monthly Business Cycle Developments, now renamed BusinessConditions Digest (B.C.D.). On the basis of the selected turns, themat-efficacy of the process will be evaluated and the needs for further'ointswork pointed out.am-)Oth-PROCESS OF SELECTIONurelyandBituminous coal production, 1914—38, is a series with a good numbermed.of turning point problems, such as the presence of strong randomlessand other irregular movements (strikes), of double turns, and of:ima-minor cycles. In addition, itis a series that has been analyzed andir bydiscussed in detail by Burns and Mitchell in Measuring Business Cycles.The seasonaly adjusted series, several smoothed versions, and tenta-con-tive as well as final turning points are presented in Chart 3. The lowestativecurve on the chart shows the time series of seasonally adjusted data.TheThe three other curves represent the results of several smoothing proc-ss atesses—a twelve-month moving average, a fifteen-month Spencer curve,7rizesand a four-month moving average, respectively. These three curvestionare used in the gradual approximation of turns in the unsmoothedseries. The essential steps of the procedure are outlined in Table 1.y inEXTREME OBSERVATIONSsthlySince the representations of trend-cycle movements should be free of,uterthe influence of extreme observations, the identification of such obser-pter.vations and the derivation of suitable replacement values are the firsttand-steps in the program.ities,Extreme values are defined as values whose ratios to a fifteen-month.tilityn ofThis is a complex graduation formula, a weighted moving average with theformhighest weights in the center and negative weights at the ends, which ensures thatmildthe curve follows the data closely. Spencer curves can be considerably morelionsflexible than an unweighted twelve-month moving average. This implies that theiringSpencer curve follows the original curve into peaks and troughs without drasticforeffects on the location of turning points—a valuable feature for a procedure ofativeturning point selection. On the other hand, the flexibility of the Spencer curve.ech-causes it to follow minor fluctuations of less than cyclical importance and some-medtimes negligible amplitude. The latter feature may complicate the selectionC00process, particularly if the procedure does not contain specifications for mini-mum amplitudes. Both curves are used in the present procedure. BITUMINOUS COAL PRODUCTION AND MOVING AVERAGES, 1914-38MiHionnettonsMitlion net tonsI1914'16'18'20'28'30'32'34'36Note:Broken vertical lines denote business cycle peaks; solid vertical lines denote business cycle troughs. 21TABLE 1PROCEDURE FOR PROGRAMMED DETERMINATIONOF TURNING POINTSI. Determination of extremes and substitution of values.II. Determination of cycles in 12-month moving average (extremes replaced).A. Identification of points higher (or lower) than S months on eitherside.B. Enforcement of alternation of turns by selecting highest of multi-pie peaks (or lowest of multiple troughs).III. Determination of corresponding turns in Spencer curve (extremes replaced).A. Identification of highest (or lowest) value within ±5 months ofselected turn in 12-month moving average.B. Enforcement of minimum cycle duration of 15 months by elimi-nating lower peaks and higher troughs of shorter cycles.IV. Determination of corresponding turns in short-term moving average of 3 to6 months, depending on MCD (months of cyclical dominance).A. Identification of highest (or lowest) value within ±5monthsofselected turn in Spencer curve.V. Determination of turning points in unsmoothed series.A. Identification of highest (or lowest) value within ±4 months, orMCD term, whichever is larger, of selected turn in short-term movingaverage.B. Elimination of turns within 6 months of beginning and end of series.C. Elimination of peaks (or troughs) at both ends of series which arelower (or higher) than values closer to end.D. Elimination of cycles whose duration is less than 15 months.E. Elimination of phases whose duration is less than S months.VI. Statement of final turning points.preliminary unadjusted Spencer curve (Spencer curve A) are outsidea specified range. The present exclusion criterion is 3.5 standard devia-tions of the ratios, and is shown as "control limit =3.500"on the titlepage of the output. The preliminary Spencer curve A is found in Out-put Table 2-2. The size of one standard deviation (7.853) is givenat the bottom of this table, and the identification of extreme valuesis made in the subsequent lines. In the present case three values, allof them strike-related, are considered extreme: November 1919, MarchZ1922, and April 1922—that is, all three of them deviate from Spencercurve A by more than 3.5 standard deviations. At the dates mentioned,the values of the unadjusted Spencer curve A are substituted for theextreme values in the original series in order to derive revised trend-cycle representations, i.e., Spencer curve B (not included in the output Cyclical Analysis of Time Seriestables but presented in Chart 3) and a twelve-month moving average.8Note that July 1922, which has practically the same value as April1922, is not excluded as extreme. The reason is that the unadjustedSpencer curve is much lower in July than in April (the value of whichis strongly affected by the high extreme value of March), and thus theratio of the July value to the Spencer curve value is less than 3.5 stand-ard deviations from the mean of the ratios. In principle, an iterativeprocedure could lead to more consistent exclusions.TURNS IN THE TWELVE-MONTH MOVING AVERAGEThe first curve from which turning points are determined, after adjust-ment for extreme values, is a twelve-month moving average (see Out-put Table 2-3 and the first curve in Chart 3). The reason for startingwith the twelve-month moving average rather than with the Spencercurve is that the Spencer curve proved to be too flexible for our pur-pose (i.e., it contains too many minor fluctuations). The two curvescan be compared in Chart 3. Most of the short fluctuations of theSpencer curve (1916, 1917, 1921, 1925—26, 1930—31, 1933, and1935)arenot reflected or only mildly reflected in the twelve-monthmoving average. Thus the latter curve seems to be a convenient meansfor eliminating fluctuations of subcyclical duration or of very shallowamplitude.The selection of turning points is done in two steps: First, tentativeturns are established, then these turns are tested for compliance witha set of constraint rules. Any month whose value is higher than thoseof the five preceding months and the five following months is regardedas the date of a tentative peak; analogously, the month whose valueis lower than the five values on each side is regarded as the date of atentative trough. In the case of bituminous coal production, the pro-gram picked a considerable number of such local maxima and minima,to wit, eight peaks and ten trough (see relevant output table). Theturns selected on the twelve-month moving average are subjected toonly one test—a check on the proper alternation of peaks and troughs.The elimination of multiple turns is simple. Of two or more contiguouspeaks, the highest one (and if they have the same value, the latest)Experiments with alternative substitution rules, such as the replacement ofextremes by the average of the nearest nonextreme values, led to the same orsimilar final results in practically all instances. Therefore, computations basedon alternative substitutions were dropped from the procedure.A 23survives; and the analogous rule holds for troughs. In the present ex-ample, the excess troughs of September 1916 and April 1935 are re-moved (see Output Table 2-5). The remaining turns are marked byan X, the eliminated ones by an E in Chart 3.TURNS IN THE SPENCER CURVEThe next step in the process is the determination of tentative and finalcyclical turns in the Spencer curve. The Spencer curve is selected asthe first intermediate curve because its turns tend to be closer to thoseof the original data,° a desirable step toward the final goal.In principle, the program searches—in the neighborhood (delineatedas ± five months) of the turns established for the twelve-month mov-ing average—for like turns on the Spencer curve. That is, in the neigh-borhood of peaks, it searches for the highest of the eleven points onthe Spencer curve; in the neighborhood of troughs, for the lowest. TheSpencer curve turns thus located are subjected to two tests: (1) liketurns must be at least fifteen months apart; and (2) the alternationof peaks and troughs must be maintained.The stipulation that turns must not be closer than six months fromthe end of the series is, of course, introduced to avoid spurious highsor lows that have no cyclical significance. In the present illustration,the search did not turn up a Spencer curve peak that correspondedto the local maximum of April 1914 on the twelve-month movingaverage. This is expressed in the message "First turn is too near thebeginning." Note that the search located a Spencer curve trough corre-sponding to the twelve-month moving average low of July 1938. TheSpencer curve turns located by the described procedure are then listed.The next test is designed to enforce a minimum-duration rule forrecognized cycles. The adopted rule is that peaks as well as troughsmust be at least fifteen months apart from like turns. After identifyinglike turns that are too close, the program excludes the lower of twopeaks and the higher of two troughs. Exclusion of any turn requireselimination of an opposite turn to maintain the proper alternation ofpeaks and troughs. Sometimes this presents no problem. However, ifthere are several corresponding turns less than fifteen months apart,9Theequal-weight scheme of the twelve-month moving average can distortthe location of turning points considerably. Compare, for instance, the turns inthe twelve-month moving average, in the Spencer curve, and in the original dataaround the 1927 peak or the 1932 trough of the bituminous coal series. Cyclical Analysis of Time Seriesa procedure must be used that will eventually lead to the eliminationof several peaks and troughs. In the present example, no cycles onSpencer curve B are eliminated because of insufficient duration. Thisis almost entirely due to the use of the twelve-month moving averageas a preliminary screening device. If the procedure had started withthe Spencer curve, several of the short fluctuations mentioned beforewould have been provisionally recognized and later excluded under thefifteen-month duration rule.The last test is designed to avoid "crossovers." If a contraction inthe twelve-month moving average is less than ten months long, thesearches for peaks and for troughs on the Spencer curve overlap.Hence the searches could conceivably lead to a Spencer curve contrac-tion in which the low precedes rather than follows the peak. Since theconditions leading to such a crossover throw doubt on the existence ofa genuine contraction, both turns involved are omitted.The remaining turning points in the Spencer curve are listed in the out-put tables and were marked by us in Chart 3. It will be useful to reviewthe efficacy of the procedure up to this point. On the whole, the de-lineated cycles seem reasonable; in particular, the omission of mostof the briefer fluctuations should be regarded as successful. The onlyproblem is the recognition of the brief 1934 contraction as cyclicallysignificant, whereas the 1935 contraction is not recognized. The me-chanics of the selection process are clear enough: The twelve-monthmoving average did not have a peak in the winter of 1934—35, andthis eliminated April 1935 as a (multiple) trough. Thus the year 1935did not fall into the search range of the program. The consequencesof this restriction will be reflected in the final turning point determina-tion, as will be seen later on.IMMEDIATE NEIGHBORHOODS OF FINAL TURNSIt could be argued that the Spencer curve cycles should form the basisof cyclical analysis, since conceptually they are closest to the trend-cycle component of the observed values. However, as in all long-termmoving averages, Spencer curves tend to shift turns, affect slopes, andconvert irregular fluctuations into smooth wavelike patterns. Thus,analysis cannot be based on smoothed series alone, but must considerthe behavior of unsmoothed observations.10 Moreover, the exclusiveuse of smoothed series would not only make cyclical analysis depend-10Fora discussion of thisproblem,see Burns and Mitchell, op.cit., pp. 310if.A 25ent upon the particular smoothing term and weighting scheme butwould also be a radical departure from cycle measures previously usedby the National Bureau and other investigators, and would impaircomparability of research results. Cycles, as analyzed by the NationalBureau, are based on unsmoothed values. Thus the search has to cod-tinue for values close to the Spencer curve tunis that are peaks ortroughs in the original seasonally adjusted data. This search could becarried out in the neighborhood of Spencer curve turns without useof any further intermediate curve, but there are possible drawbacks tosuch a procedure. The Spencer curve is a long-term moving average,quite capable of imparting a bell-type smoothness to data that formdouble or triple peaks or troughs (compare the curve contours in 1916,1917, 1921, and 1935). Hence, the turns in the original data mightbe quite far from those of the Spencer curve, and consequently theprocedure would require a correspondingly broad search range inorder not to miss the turns. However, such a wide range would catchirregular maxima or minima that are not cyclically significant peaksand troughs. For this reason it was thought better to redelineate theneighborhood of the final turns by searching in the neighborhood ofthe Spencer curve turns for corresponding turns in a short-term mov-ing average.A curve thatrepresentstheoriginalseasonalyadjusted datasmoothed by a short-term average is the MCD curve. MCD stands formonths of cyclical dominance. The MCD of any series is the numberof months required for the systematic trend-cycle forces to assertthemselves against the irregular time series component. If a series hasstrong cycles and little irregularity, it will not take long (perhaps notlonger than one or two months) until the average change in the trend-cycle component exceeds the average change in the irregular compo-nent. If a series has shallow cycles but is very choppy, it may takemany months before the cyclical movement asserts itself. In the firstcase no smoothing, or smoothing by only a very short-term average,is required to bring out the cyclically relevant movements; in the sec-ond case a correspondingly longer term is needed.'1 The MCD curveis the curve representing the data smoothed by the MCD term appro-11 Technically, the number of months required for dominance of the cyclicalover the irregular component is that span over which the average change in theirregular component becomes smaller than the average change in the trend-cyclecomponent. For further explanation, see Julius Shiskin, "How Accurate?" Ameri-can Statistician, October 1960, pp. 15 if. Cyclical Analysis of Time Seriespriate for the relationship of trend-cycle and irregular movements inthe analyzed activity. In order to reduce the effect of irregular changesand the influence of remote values, the span of the smoothing termused is confined to the narrow range of three to six months. For meas-ured MCD'S of one and two months, a three-month term is applied; forMCD'S of seven or more months, a six-month term is used.The MCD for bituminous coal production is four months. The MCDcurve is plotted as the third curve of Chart 3 and is based on OutputTable 2-4. The method of deriving turning points in the four-monthmoving average is practically the same as that described in the preced-ing section. Turns are determined by selecting the highest peak on theMCD curve within a span of five months from the dates of the peakson the Spencer curve; MCD troughs are analogously selected. Beforethis determination is made final, turns at the very beginning and endof the MCD series are omitted, the minimum duration rule is enforced,and the turns are tested for crossovers. In the present case, no furtherexclusions result from the application of these tests. The remainingturns are reported in the output table as turning points in four-monthmoving average; they are marked by crosses on the third curve ofChart 3.SELECTION OF FINAL TURNING POINTSThe last step of the procedure is to find the peak and trough. valuesin the unsmoothed data that correspond to the MCD turns previouslyestablished.'2 This simple search is analogous to the previous transi-tions (from turns in the twelve-month moving average to Spencer curveturns and from Spencer curve turns to MCD curve turns). The programestablishes the highest values in the unsmoothed data within a spanof ± MCD or ± four months (whichever is longer) from the peak inthe MCD curve; correspondingly, the lowest value of the unsmootheddata in the neighborhood of MCD troughs is established. No turns closerthan six months from the ends are accepted. Also, the first and lastpeak (or trough) must be at least as high (or as low) as any valuebetween it and the end of the series. The resulting turns are reportedin Output Table 2-8.12Againit could be proposed that the dates and values of the MCD turns shouldbe regarded as those relevant for cyclical analysis, since the unsmoothed seriesis modified by irregular elements that are not intended to affect cyclical measures.Whatever the merits of this view, the present analysis ignores it in order to adhereas closely as feasible to standard practices.A 27The final tests deal with the duration of cycles and cycle phases.Full cycles (peak-to-peak and trough-to-trough) are checked for aminimum duration of fifteen months. The fact that this criterion wasapplied earlier to the trend-cycle curve does not necessarily mean thatthe related cycle in the unsmoothed data satisfies the condition, as theactual initial and terminal turns can be closer than the related turnson the Spencer curve. In the present example, however, the applicationof the test does not lead to further exclusion of cycles. The last con-straint for which the turning points are tested is a five-month minimumrule for phase durations. There is no equivalent rule in the standardanalysis of the National Bureau. However, early experiences showedthat some sharp, short episodic movements (such as strikes) can be re-distributed by the various moving averages into fluctuations of cyclicalcontours and durations. The minimum-phase-duration rule, which atpresent is set at five months, is a possible remedy.13 This rule could bereadily modifiedif experimentation or extended experience shouldprove it to be inadequate.The final turning points are listed on Output Table 2-8 and markedby crosses on the lowest curve of Chart 3. Comparison with thosepreviously selected,14 and marked by squares on the same curve showsone minor and one major discrepancy. The minor difference consistsin the selection of April 1922 instead of July 1922 as a trough. Thesituation here is that of a characteristic double trough. The earliertrough, in April, is slightly lower and thus was selected under thespecified procedures.'5 The difference is unimportant and could bepassed over without comment were it not that it illustrates some char-acteristics of programmed turning point determination. The NationalBureau's selection of the July turning point is explained as follows:The trough in 1922 exemplifies a "double bottom." There is a deep troughin April 1922, when a strike—probably the greatest in the history of thisafflicted industry—broke out. A slight revival occurred during the next twomonths, and a relapse in July, when the railroad shopmen's strike produced13 Different minima for expansions and contractions were considered, in viewof the longer durations of expansions in historical business cycles, but were ruledout in order to make the program equally effective for series with positive andinverted conformity and for series with rising and falling long-term trends.14 Burns and Mitchell, op. cit.,pp.60 if.'5 April 1922 was identified above (p. 21) as an extreme value. This does notprevent it from being chosen as a turning point. Prevailing practice is to acceptextremes as turning points if they occur in a turning point neighborhood. Cyclical Analysis of Time Seriesan acute car shortage in the non-union field. The seasonally adjusted figureis fractionally higher in July than in April (20.2 against 20.1 million tons).But the difference is negligible, and in line with our rules, the trough isdated in the later month.'6Apart from the consideration of historically unique events, such asthe two strikes, it would be difficult to program a provision to neglect"negligible" differences. When is a difference negligible? Should thesame standard be applied to all series, whatever their volatility? And ifthere are several alternative troughs, each negligibly different from theother but arranged in ascending order, should the last one neverthelessbe selected? While it is not technically impossible to incorporate theseand similar considerations in a programmed selection, it would lead toa proliferation of tests that might make the process unwieldy and per-haps impractical—at least at the present state of the art.The major discrepancy between the traditional and the programmedturning point determination is the recognition by the programmedprocedure of a cyclical contraction in 1934. The problem is not onlythe debatable recognition of any contraction at all but the specificationof the contraction as lasting six months, from March to September1934, instead of lasting for one more year, to September 1935. Thelatter would be the more plausible version, in view of the behavior ofthe actual data. The technical reason for the programmed determina-tion was discussed before in connection with the turning point selec-tion on the Spencer curve. It goes back to the use of the twelve-monthmoving average as the first step in the process of cycle identification.It would, of course, be quite simple to increase the flexibility of thefirst average, decrease the span, and thus permit consideration of theevents of 1935. Alternatively one could decrease the flexibility of thefirst curve, and thus eliminate the cycle in question altogether. What-ever the solution to the problem, its formulation and acceptance can-not be based on the analysis of programmed turning point determina-tion for a single series or even for a few series. It is always possible,and relatively easy, to modify the program to cover a small numberof contingencies. The goal is to develop rules that operate in a satis-factory manner for most economic time series. Thus, experimentationwith a fairly large sample of series must be resorted to in order toestablish the efficacy and the shortcomings of a given set of rules.i6Burnsand Mitchell, op. cit., p. 63. 29Analysis of programmed turning points and modification of proceduresmust be based on experiences with such a sample. This is the concernof the following section.EMPIRICAL EVALUATION OF PROCEDUREDESCRIPTION OF SAMPLEThe sample chosen for the experiment is the collection of leading,lagging, and coinciding business cycle indicators for the period starting1948, as published monthly in Business Cycle Developments.'7 Thereare several reasons for this choice. First, the sample covers a largenumber of important activities representing various aspects of economiclife in the United States. Second, the selected series exhibit a greatvariety of behavior: there are series with relatively large random com-ponents and little trend, such as temporary layoffs; there are smoothseries, with little random and strong upward trend, such as personalincome; there are positively conforming series, and there are invertedseries; there are monthly and quarterly series; there are series withand without negative entries. Third, the series were all available, in up-to-date and seasonally adjusted form, in Business Cycle Developments,thus reducing or eliminating the chores of data collection and seasonaladjustment. Fourth, and for present purposes most important, cyclicalturning points have already been established by the National Bureaufor all these series, based on the rules given by Burns and Mitchell inMeasuring Business Cycles. This makes comparisons of previously se-lected and program-selected turns possible for all series. Business CycleDevelopments reports thirty leading, fifteen coinciding, and seven lag-ging indicators, or fifty-two altogether. One series, new approved capi-tal appropriations (series 51), had to be omitted because of severaldiscontinuities. Thus, fifty-one series were left for experimentation—asufficiently large and variegated sample for present purposes.Despite its broad coverage, the sample described has one seriousbias that may affect its value for testing the broad applicability ofprogrammed turning point determination for economic time series ingeneral. The bias arises from the fact that most of the series shownin Business Cycle Developments were chosen because their marked"Thesample used was published in Business Cycle Developments before thechanges instituted in the April 1967 issue. Cyclical Analysis of Time Seriescyclical characteristics made the series valuable for diagnosis of cur-rent business conditions. That is, most of these series have recog-nizable if not pronounced cycles, show good conformity to severalbusiness cycles, and are not excessively affected by random elements.The greatest difficulties in turning point determination arise whencyclical components are weak and irregular factors are strong—andthis situation is rare in the selected sample. However, at the presentstage of development the programmed approach cannot be expectedto solve problems that proved intractable before. Thus, although thesample excludes series whose cyclical behavior is particularly uncer-tain, it will serve well to test the broad applicability of the approachand to suggest the direction in which further progress should besought.CRITERIA FOR EVALUATIONBefore reporting the outcome of the experiment, it might be well toconsider the criteria by which the results should be evaluated. Anobvious standard for evaluation is the turning point selection that hadpreviously been made for these series. Although for many reasons—particularly comparability with previous work—this appears to be adesirable standard, it is not without weaknesses.For one thing, the general rules of turning point determination aresubject to interpretation; and, if a basic rule permits more than onechoice, the choice actually made in the past should not serve as cri-terion for the evaluation of the programmed selection. Second, in theselection and analysis of cyclical indicators, doubtful cases might havebeen resolved by accepting fluctuations that conformed to fluctuationsin business activity at large.1' Thus, neither the programmed selectionof additional intraphase turns nor the omission of conforming butotherwise doubtful phases should necessarily be regarded as a defectof the program. Third,itis possible that the technology of pro-grammed selection requires somewhat different rules than those de-veloped as guides for the exercise of judgment by individuals. Thus,there exists the possibility that the ground rules may have to bechanged to facilitate programmed selection. Such changes should, ofcourse, be made only if clearly justified by the results of broad experi-mentation.The preceding remarks should not be interpreted as a defense ofBurnsand Mitchell, op. cit., p. 58.A 31the programmed selection of turns whenever these depart from thosepreviously determined. After all,the program is experimental andexcludes from consideration certain criteria, such as comparative am-plitude and runs of changes in the same direction, which proved to bevaluable guides in the past. It is precisely the purpose of this reportto establish whether programmed selection can safely ignore some ofthese guides or whether the program must be amended to reflect theseand other considerations. The most important criterion for the generalusefulness of the program is whether basic research findings areaffected by its use.PROGRAM-DETERMINED AND STAFF-DETERMINED TURNSIn Chart 4, the turns picked by the program are marked by crossesplaced close to the line and those chosen previously by the Bureau aremarked by squares. Even a casual examination of the chart revealsthat in most instances the program picked the same points as thoseestablished earlier, but that the program often recognized a numberof short and mild fluctuations as cyclical that were not so regardedin previous analyses. The opposite situation, that of fluctuations recog-nized previously but not by the program, occurs less frequently. Incomparing the results, a distinction must be made between the identi-fication of specific cycles, and the precise dating of their turns. Thefirst implies the recognition of certain neighborhoods as turning pointneighborhoods; the second involves specification of the month in whichthe turn occurred. Let us begin with the question of recognition.In the following analysis, interest is concentrated on the differencesbetween the results of programmed and nonprogrammed determina-tion of turning points. Table 2 shows that the program found 432specific phases, as against 384 found by the nonprogrammed approach.Identical phases were found by both approaches in 346 cases. Thatmeans the program found 90 per cent of the phases previously estab-lished by the National Bureau staff. Since the program found 48more phases than the Bureau, the phases found by both approachesconstitute only 80 per cent of all phases determined by the programmedapproach.The net difference of 48 does not provide a satisfactory criterionfor evaluating the similarity of the results. The net difference hidesthe fact that there are 124 phases that were chosen by one approach Cyclical Analysis of Time SeriesCHART 4BUSINESS CYCLE INDICATORS, TURNING POINTSSELECTED BY PROGRAMMED AND NONPROGRAMMEDLeading IndicatorsAPPROACH, 1947-67 DDD5D5D50Leading IndicatorsProgrammed Selection of Turning PointsCHART 4(Continued)33 Leading IndicatorsCyclical Analysis of Time SeriesCHART 4(Continued)A CHART 4(Continued)Leading Indicators35 CyclicalAnalysis of Time SeriesCHART 4(Continued)Leading Indicators 37CHART4(Continued)Leading Indicators CyclicalAnalysis of Time SeriesCHART 4(Continued)LeadingIndicators 39CHART4(Continued)CoincidingIndicators1IIIIIIIIIIIIIIII60'I30. Employees, nonagricultu.'aI establishments55IC50II51I7570IIIIIII31. Total nonagricultural employmentIIIIIIIIIIIIIIIIIIIIII32. Unemployment rate, totalper cent, inverted scale)aIIIIIIIIIIIIIIIIIIIIIIII1947'50'55'60'65'67 CoincidingIndicatorsCyclical Analysis of Time SeriesCHART 4(Continued) 41CHART 4(Continued)Coinciding Indicators Cyclical Analysis of Time SeriesCHART 4(Continued)CoincidingIndicators 43CHART4(Continued)LaggingIndicators11IIIIliiiIIIIIii'iSO44. Business eapenditures, new plant and equipment, 0II-130SI0IIIIJ20IIIIIIIII45. Labor cost per unit of output, manufacturing (1957-59 = 1001IiIIhOI1105I-1(00aI-195a*SII-190-1B5IIi75aIII46. Labor cost per dollar of real corporate GNP, 0 (1957-59 = 10011(51110II-1105x*-booIIaa-j95aIIIII75IIIIIIIIIIIII(IIIIIIIIIIIIIIIIII1947'50'55'60'65'67 IndicatorsCyclical Analysis of Time SeriesCHART 4(Concluded)Note: Crosses denote program determined turning points of the specific series;squares denote turning points of the specific series previously determined by theNational Bureau staff. Broken vertical lines denote business cycle peaks; solidvertical lines denote business cycle troughs. TABLE 2SPECIFIC-CYCLE PHASESIN BUSINESS CYCLE INDICATORS,PROGRAMMED AND NONPROGRAMMED APPROACHES,1947—67Expan-sionsContrac-(ionsAllPhases1. All specific phases found by programmed ap-proach2142184322. All specific phases found by nonprogrammedapproach1861983843. Specific phases found by both programmed andnonprogrammed approacha1661803464. Specific phases found by programmed but not bynonprogrammed approach4838865. Specific phases found by nonprogrammed but notby programmed approach2018386. Phases found by both approaches as a percentageof those found by nonprogrammed approach8991907. Phases found by both approaches as a percent-age of those found by programmed approach788480Source: Chart 4.a Phaseswith correspondinginitial and terminal turning points only.but not by the other—86 by the program but not by the NationalBureau staff, and 38 by the staff but not by the program. On the otherhand, the differences shown in the table overstate the differences inthe results of the two approaches. Phases are regarded as correspond-ing only if both the initial and the terminal turning points correspond.That is,if the program finds an intermediate contraction during acyclical upswing of the nonprogrammed approach, this is counted asfour differences—three extra phases found by the program and oneextra phase found by the National Bureau staff. An example can befound to illustrate this point in the first expansion of the averageworkweek series, the first series shown in Chart 4. Here the contrac-tion found by the program in 1951 gives rise to the report of fournoncorresponding phases, i.e., of the three phases found by the pro-gram (1949—51, 1951—51, 1951—53) and the noncorresponding ex-pansion found by the National Bureau staff for 1949—53.45 Cyclical Analysis of Time SeriesTABLE 3CYCLICAL COUNTERPHASESIN BUSINESS CYCLE INDICATORS,PROGRAMMED AND NONPROGRAMMED APPROACHES,194 7—6 7Specific phases found by both programmed andnonprogrammed approach346Counterphases found by programmed but notby nonprogrammed approach40Corresponding to business cycle phases8Not corresponding to business cycLe phases32Corresponding to business cycle retar-dations19Counterphases found by nonprogrammed butnot by programmed approach14Corresponding to business cycle phases8Not corresponding to business cycle phases6Corresponding to business cycle retar-dations1Note: Counterphases are extra expansions (contractions) according to oneapproach, while the series experienced a contraction (expansion) according tothe other approach. Extra turns, found by an approach at either end of a series,imply counterphases; these are included in the numbers given above.In order to avoid the quadruple counting, Table 3 is introduced.This table reports only counterphases, that is, contractions (or expan-sions) that are found by one approach during expansion (or contrac-tion) phases found by the other. In the fluctuations of the averageworkweek between 1949 and 1953, only one counterphase occurs—the extra contraction found by the program during 1951. The sum-mary shows that the program found only forty counterphases. More-over, eight of these correspond to concomitant business cycle phasesand nineteen to the major retardations in business activity that oc-curred during 1950—5 1, 1962—63, andThus, most of thecounterphases found by the program are economically plausible. Thecounterphases found by the nonprogramnied approach amounted toonly fourteen, with eight phases conforming to corresponding businesscycle phases and one to the retardation of 1950—51. This means that,Theseneighborhoods were singled out since many leading and a fair numberof coinciding indicators showed declines, or at least retardations. 47with only a few exceptions, the National Bureau staff agreed with thecyclical direction implied in the programmed determination of specificcycle phases.When additional phases, such as the specific contraction from 1952to 1953 in manufacturers' inventories of finished goods (series 48),are recognized by the program, the basic reason is simply that thetwelve-month moving average went down long enough to establish ahigh and a low, each in the center of an eleven-month period. Whena contraction recognized by inspection is not chosen by the program,as is the case in the specific decline from 1960 to 1961 in the sameseries, the reason is that the twelve-month moving average did not godown or did not go down long enough to qualify the decline as a cycli-cal contraction under the adopted criteria. It is true that other rules(alternation of peaks and troughs, minimum cycle length, minimumphase length, etc.) affect the final selection of turns, but the behaviorof the twelve-month moving average controls basic eligibility. One casewhere the program omitted a phase selected by the National Bureaustaff—because of insufficient duration, although the twelve-monthmoving average shows cycles—is the 1952 expansion in vendor per-formance (series 27).The cited examples of differences in cycle recognition, and othersthat could be easily adduced, raise the question whether the pro-grammed or the previously determined cycles are analytically prefer-able. This question is hard to answer without formal standards or atleast some guiding considerations. In the case of manufacturers' inven-tories (series 48), the program-selected extra contraction of 1952—53exceeds the extra contraction of 1960—61 selected by the Bureau staffin length and in amplitude and thus seems a better choice. The Bureaustaff's recognition of the 1960—61 movement as a cyclical decline waspresumably influenced by the fact that it corresponds to a businesscycle contraction. On the other hand, the program's recognition ofan extra contraction during 1956—57 in the layoff rate(series 4)seems inferior to the judgment of the staff member who regarded1955—58 as one long specific expansion.2°20Theprogram's recognition of the additional contraction was partly a con-sequence of unsatisfactory dating of turns—a point which will be discussed lateron. Proper dating of the trough of the (inverted) layoff rate in November 1955would have ruled out recognition of the ensuing increase as an expansion becausethe period of increase would have been below minimum phase duration. Cyclical A nalysis of Time SeriesOnly five of the forty counterphases found by the program must becharacterized as incompatible with a reasonable interpretation of thebasic rules. The counterphases shown by series1in 1962—63, series15 in 1963—63, series 33 in 1956—57, series 42 in 1948—49, and series50 in 1961—62 are minor movements in comparison with the typicalcyclical variations exhibited by these activities. All other extra-phasesconsist of mild fluctuations with fairly clear cyclical characteristics.The acceptability of such mild movements as cyclical phases dependson research goals and perhaps on the economic characteristics of ex-periences during the historical period analyzed. If one is interested inthe timing and the degree of synchronization of fluctuations in eco-nomic activities during recent years, one may have to recognize mildfluctuations since they are the only ones present. In fact, analyticalinterest is shifting to the timing of changes in growth rates, so thatanalysis of fluctuations is not limited to actual declines in the levelof activities. On the other hand, recognition of mild fluctuations maywell be less desirable—or less important—for research concerned witheconomic fluctuations during the period before World War II. In prin-ciple, the program could be modified to accommodate these differencesin objectives and historical context. However, such modification woulddiminish the procedural stability necessary for a uniform derivationof cyclical turning points and would thus be undesirable.The above comparisons dealt with the recognition of cycle phases.Table 4 deals with the comparison of program-determined and staff-selected cyclical turns for leading, coinciding, and lagging indicators.Altogether, the difference between the results of the two approachesamounts to about 20 per cent of all phases, with a clear tendency ofthe program to pick more turns.The program found 483 turns in the series as compared with 435selected by the Bureau staff, for a net difference of 48 turns, or 11per cent of the previously selected turns. These figures, however, over-state the agreement of the two selections since the program picked 72turns where no corresponding turns were recognized by the NationalBureau staff, and the staff picked 24 turns where no correspondingturns were found by the program. The resultant sum of 96 discrepan-cies in turning point recognition is double the size of the net differ-ences. The program tended to recognize more cyclical turns both inleading and coinciding indicators, but particularly in the leading groupwith its more volatile activities. Altogether, the 411 corresponding 49TABLE 4CYCLICAL TURNING POINTSIN BUSINESS CYCLE INDICATORS,PROGRAMMED AND NONPROGRAMMED APPROACHES,19 47—6 7Indicators29Leading14Coinciding6LaggingAllIndicators1. All turns found by programmedapproach324103564832. Allturnsfoundbynonpro-grammed approach28198564353. Corresponding turns found bybothprogrammedandnonpro-grammed approachesa. Identical dates27225592924747411394b. Different dates1700174. Noncorresponding turnsa. Found by programmed butnot by nonprogrammed ap-proach5211972b. Found by nonprogrammedbut not by programmed ap-proach969245. Corresponding turns as a per-centage of those found by nonpro-grammed approach946. Identical turns as a percentageof those found by nonprogrammedapproach917. Corresponding turns as a per-centage of those found by pro-grammed approach858. Identical turns as a percentageof those found by programmed ap-proach82turns constitute 94 per cent of all turns found by the nonprogrammedapproach and 85 per cent of the more numerous turns found by theprogrammed approach.While there are systematic differences between programmed andunprogrammed cycle recognition, differences between the dates of Cyclical Analysis of Time Seriescomparable turns selected by the two approaches are of minor im-portance. This can be seen in Chart 4 and lines 3a and 3b of Table 4.shcAmong 411 cyclical turns that are recognized both by the programlatiand by inspection, the program picked the same date in 394 turnsrec(96 per cent of all corresponding turns); this represents 91 per centof all staff-selected turns and 82 per cent of all turns found by the pro-grammed approach.trotIn 12 of the 17 turns with different dates—which all occurred in theHeleading indicators—the National Bureau staff picked later turns thanthethe program, in keeping with the Bureau's preference for resolvingbetdoubtful cases in favor of the later turn. Only four program-establishednotdates are clearly inferior. They occur in the following circumstances:itregTypeDate ofDate ofCauseSeriesActivityofProgram-Staff-Selectedfor ProgramTurn Selected TurnTurnSelectionpre2Accession rateTJune 1963Nov. 1963Lower Spencercurvealte4Layoff rateTaMay 1955Nov. 1955Lower Spencerelmcurve6Initial claims,F'Aug. 1949Apr. 1949Higher peakin istate unem-ploymentinsuranceWh27Vendor per-TMar. 1957Dec. 1957Lower SpencerlishiformancecurveaShownas peak on inverted scale.Ofb Shown as trough on inverted scale.Wii(In three of the four instances the basic cause for the discrepancythewas that the Spencer curve was lower in the neighborhood of theof eprogram-selected trough; and the staff-selected trough (which was lowerprojand/or later in the unsmoothed series) was beyond the stipulatedcidijsearch range. In series 2, for example, the program picked a turn incycithe middle of the flat-bottom trough of 1963 although there is a lowerseriipoint at the end of the year—the turn picked by the National Bureaugrasstaff. The reason is that the Spencer curve has its trough in the be-projginning of the year, which puts the December low of the three-monthrecemoving average and the November low of the unsmoothed series be-allA ProgrammedSelection of Turning Points51yotldthe respective search ranges. The search range, from Spencer toshort-term average, would have to be greatly increased to catch thelate 1963 low. However, such an increase would also result in amsrecognition of the irregular high in December 1959 as a peak, a clearlyundesirable result. The limited range of the search leads to a ques-tionable selection also in case of the peak (shown on the chart as atrough, due to inverted scale) of initial claims (series 6) in 1949.theHere the program chooses the middle value of three prongs althoughIanthe last value is higher and the early value, chosen by the staff, isingbetter supported by adjacent values. The programmed approach didiednot search as far as the last prong and did not choose the first becausees:it always picks the outlying value of the unsmoothed data withoutregard to adjacent values.Application of the process to other series than those used in thepresent study revealed a potential weakness. In excluding turns asso-ciated with "short" phases (less than 5 months), the alternative peaktcerselected by the program may be lower than the eliminated one, or thealternative trough may be higher. This result would be justified if theIcereliminated turn were randomly high or low but not if it reflected acyclical reversal. Further experience may lead to program modification;in the meantime the user should be aware of the problem.On the whole, our experience suggests that programmed turningpoint determination will prove useful for many research purposes.While the program-determined turns may be inferior to those estab-icerlished by experienced research workers, they may well be superior tothose found by nonspecialists. The program is objective with regardto procedure; thus, the same turns will be found by every investigatorwho relies upon the program.One research result that would not be significantly altered, whetherncythe programmed or staff-selected turns are used, is the classificationtheof economic indicators according to timing characteristics. Also, sincewerprogram-determined and staff-selected dates are identical for all coin-itedciding indicators, it must be presumed that the dating of referenceiincycles (which depends heavily on specific cycle turns in the coincidentwerseries) would not be substantially modified by the adoption of a pro-grammed selection of turning points. However, the propensity of thebe-program to pick up the relatively mild fluctuations, which characterize)flthrecent experience, affects measures of average cycle durations, over-be-all amplitudes, and so forth. Cyclical Analysis of Time SeriesAPPLICATION TO REFERENCE TURNSIn the preceding section it was established that the classification ofindividual indicators into groups of leading, lagging, and coincidingmeasures would not be affected if turns were established by the pro-grammed approach rather than by inspection. This, of course, doesnot imply that identical turns are selected by the two methods.In this section we wish to establish whether and to what extentmeasures, such as cumulative historical diffusion indexes,21 are affectedby the substitution of program-determined turning points for staff-Kselectedones. A particularly important aspect of this question relatesto summary measures of coinciding indicators, since their turns areKstrategicdeterminants of reference turning points, i.e., of the bench-mark dates chosen to identify peaks and troughs in business activity atKlarge.If it should turn out that cyclical turning points in cumulativediffusion indexes of coinciding indicators, based on program-deter-mined specific turns, conform well with turns established by inspection,then the programmed approach may become a tool for reference turndetermination. Finally, since the program tends to select more cyclesthan does the previous Bureau approach it would be interesting toestablish whether these additional cycles—similar to cycles corre-sponding to those selected by inspection—are sufficiently synchro-nized to lead to recognizable swings in the cumulative diffusion in-dexes; and if so, whether these extra swings are related to knownperiods of business retardation.The evidence is presented in Chart 5 and Table 5. The chart showsKthat,with the exception of one contraction, the two sets of cumulative21 Broadly defined, "diffusion" indexes for a group of time series consist ofthe percentage of these series which are increasing over a specified time span:they measure the degree to which the increases are diffused among the com-ponents. In "historical" diffusion indexes, all changes between the troughs andpeaks of the component series are regarded as increases, all changes betweenpeaks and troughs as decreases. This means that historical diffusion indexesdescribe the degree to which cyclical expansion phases prevail among corn-Kponents. For "cumulative" diffusion indexes the differences between the per-centage of increasing series and 50 per cent are cumulated, on the theory thatthese differences reflect the degree of concomitance of upward movements andthus of upward thrust in the group as a whole. If the component series can beaggregated, turns of the simple diffusion indexes lead the corresponding turnsof the aggregate and those of cumulative diffusing indexes tend to coincide withthem. A basic discussion of the construction and behavior of diffusion indexes canbe found in Chapters 2 and 8 of BusinessCycleIndicators, Geoffrey H. Moore,ed., New York, Princeton University Press for NBER, 1961. iiiLeading IndicatorsIxIIIaIIxlCoinciding IndicatoaaaaIIIIIIIProgrammed Selection of Turning Points53CHART 5CUMULATIVEHISTORICAL DIFFUSION INDEXESBASED ON PROGRAM-SELECTED AND STAFF-SELECTEDCYCLICAL TURNS IN THE COMPONENTS, 1948-65*000K+6000K+1000 -K—1000-NK+1000 -(+1000-(+5000(+6000I(+5000/4IIIHandIII1948'5*'53'55'57'59'6*'63'65Note: Broken vertical lines denote business cycle peaks; solid vertical linesdenote business cycle troughs. Origin of vertical scale is arbitrary, since K maybe any constant. TURNING POINTS IN CUMULATIVE HISTORICAL DIFFUSION INDEXES, BASEDON PROGRAM-SELECTED AND STAFF-SELECTED CYCLICAL TURNS OFCOMPONENTS,194 8—65TypeofTurnBusinessCycleDates29 LeadingIndicators.75 Roughly CoincidentIndicators7 Lagging IndicatorsStaff-Program-Staff-Program-Staff-Program-SelectedSelectedSelectedSelectedSelectedSelectedPNov. 1948Sept. 1948Sept. 1948Jan. 1949Jan.1949TOct. 1949May 1949May 1949Oct. 1949Oct. 1949Mar. 1950Mar. 1950PJuly 1953Jan.1951Jan. 1951June 1953June 1953Dec. 1953Dec. 1953TAug. 1954Dec. 1953Dec. 1953May 1954 *June1954*Feb.1955Feb. 1955iJuly 1957Nov. 1955Nov. 1955Mar. 1957Mar. 1957Dec. 1957Dec. 1957TApr. 1958Mar. 1958Mar. 1958Apr. 1958Apr. 1958Sept. 1958Sept. 1958May 1960June 1959 *May 1959 *Apr. 1960Apr. 1960Nov. 1960TFeb. 1961Jan.1961Jan.1961Feb. 1961Feb. 1961May 1961LEADS (—),COINCIDENCES (0),AND LAGS (+),IN MONTHS, RELATIVE TOBUSINESS CYCLETURNSPTpTNov. 1948Oct.1949July 1953Aug. 195400+2+5+5+6+2+5+5+6PJuly 1957+5+5TApr. 195800+5+5PMay 1960+6TFeb. 196100+3Note: For an explanation of the nature of cumulative historical diffusion indexes, see footnote 21.Asterisks denote a difference between the turning point dates chosen by the two methods.j 55diffusion indexes move closelytogether,exhibiting correspondingswings, similar amplitudes, and practically simultaneous timing. Theone exception is the 1960—61 contraction in the lagging indicators,which is shown in the index based on staff-selected turns but is omittedin the index based on program-selected turns. Reference to Chart 4shows that the difference is entirely due to turning point determinationin two series (48 and 49). In these series the program does not selectturns in 1960 and 1961. The declines during these years are minuteand scarcely detectable on our chart.Table 5 quantifies the relationship of cyclical turns in the two setsof indexes to those in general business activity. The upper panel con-tains the dates of these turns: only two out of twenty-one comparableturns occurred at different dates (see asterisks), and the differencesnever exceeded one month. The lower panel focuses on the timingrelation of the diffusion index turns to those in business cycles. Notethe consistency of signs for both sets of leading and of lagging indexes;most important, note the "practical coincidence" of the turns of cumu-lative diffusion indexes of coinciding indicators, whether computerbased or not, with business cycle turns. That is, with one exceptionthe peaks and troughs of the index either coincide exactly (three outof eight) or occur within three months of business cycle turns. Theexception, a lead of four months, occurs at the July 1957 peak. Thisperformance bolsters the hope that program-based cumulative diffusionindexes of coinciding indicators—though not necessarily of the fifteenindicators used above—may play an increasing, and perhaps decisive,role in the determination of business cycle turning points.One question is whether it is possible to dispense with other evi-dence, such as amplitudes of cyclical swings and the economic im-portance of the activities reaching turns at particular dates. Also, theprogrammed method lends itself better to the identification of pastbusiness cycle turns than to the identification of current turns, sinceit requires evidence for four or more months after the occurrence ofa cyclical turn in the component series. Nonprogrammed identificationof current business cycle turns may possibly be more prompt. It canmore readily make use of other evidence, such as the behavior ofleading indicators, the sharpness of the turns, the character and corn-prehensiveness of specific activities, and the effect of impending eventsand policies.There are other applications. The program permits, for example, Cyclical Analysis of Time Seriesturning point determination and construction of historical diffusionindexes for large groups of time series, such as sales and profits dataof individual companies, or indicators of various economic activitiesin each of the fifty states. The program can also be used to measurecyclical divisions in levels and changes for business cycle analysis,trend analysis, and other purposes. In short, programmed determina-tion of turning points opens the way for a variety of imaginativeexperiments.SUGGESTIONS FOR FURTHER DEVELOPMENTExperimentation with the programmed turning point selection raisescertain issues that should be considered in the further development ofthe approach.1. The program is sensitive to the accuracy with which the basicdata are reported, that is, rounded data may yield fewer and differentturns than do unrounded data. It should be feasible to standardize theinput so that the number of digits used does not affect the number andlocation of specific cycles.2. The twelve-month moving average, used as the basis for the de-termination of the presence of cycles, may obliterate shallow but cycli-cally significant phases in certain series. Conversely, itmay transformirregular movements into cyclical patterns. If these tendenciesare tobe avoided, the smoothing term of the basic trend-cycle representationshould bear some relation to the relative importance of irregular,ascompared to systematic, movements.3. The Spencer curve, with its graduated 15-point weightpattern(and negative weights at the ends) is not necessarily themost effec-tive tool for present purposes. It may be fruitfulto experiment withother weighting systems and perhaps with flexible weights.4. The turning points near the ends of the seriesare frequentlymore uncertain than others. Some modifications of the approachmaybe considered. The span (now six months from each end) withinwhich turns are not recognized could be extended. Thistype of con-straint, which now operates only on the turning points of the final(unsmoothed) series, could also be imposedon some of the smoothedcurves. Also, the present sequence of tests(first for acceptability ofend values, then for cycle and phase durations) might be reversed,sothat those turns that become first or last turns only through there- 57jection of end turns would not be subjected to tests designed for turnsclose to the ends of the series.5. Present search ranges sometimes exclude values worthy of con-sideration as cyclical peaks or troughs. While extension of the rangesincreases the danger of selecting noncyclical extremes as turns, thereis no assurance that the present ranges are optimal. Experiments withalternative ranges might be desirable.6. Since amplitude considerations are only implicit in the presentprocedure and in some of the above suggestions, the amplitude effectsof these procedures and of contemplated changes should be kept underclose review. An explicit amplitude criterion might also be devisedand tested.7. In view of the bias inherent in the use of a collection of well-conforming indicators as a test sample, it is desirable to test the ap-proach on series that present special problems of turning point deter-mination. This will improve our judgment regarding the effectivenessof the approach for economic activities at large.It is not proposed that all of these suggestions should be evaluatedon the basis of present experience. The effects of any specific change,and the interaction of several changes, are hard to foresee. What isneeded is some well-organized accounting of the results of the presentprocedure after it has been more widely used and an evaluation ofthese results, based on well-defined criteria. When substantial addi-tional knowledge has accumulated, major changes in the current ap-proach might be contemplated. SAMPLE RUN,SELECTION OF CYCLICALTURNING POINTS,BITUMINOUS COAL PRODUCTION CyclicalAnalysis of Time SeriesBITUMINOUSCOAL PROOUCTION100.000 MEl TONS1914 —193801119NBEA TURNING POINT DETERMINATION FOR SERIES OSDSRNUMBER OF MONTHS •300FIRST MONTH •19141MCD •0CONTROL LIMIT •3.500YEAR1911191OuTput Table 2-11911BITUMINOUS COALPRODUCTION100.000 NET TONS1914 —19391911TIRE SERIES OATA011181931YEARJANFEBMARAPRRAYJuNEJULYAUGDEPTOCTNOVDEC1914393.0359.0392.0347.0340.0345.0361.0363.03T1.G325.0312.0336.00915351.0329.0324.0349.0325.0347.0354.0359.0387.0394.0430.0463.01956440.0008.0391.0408.0385.0381.0403.0397.5390.0432.0445.0YEAR1917453.0465.0489.0407.0496.0470.04A3.0447.3425.0420.0439.0444.00918398.0493.0491.0535.0531.0521.0550.0520.0493.0455.0402.0406.0091I1939070.0261.0052.0290.0254.0260.0269.0296.0317.0299.0339.0329.0191*190591*693*081081 Table 2-2SPENCERCURVE. MO SUBSTITUTIONSO1EEBYEARJAMFEBMARAPRMAYJUNEJULYAUGSEPTOCTMOVDEC1914370.3367.0360.9057.3334.6303.6353.3301.734T.3341.6336.3332.50915331.4332.0333.0334.933R.D343.7302.5365.7383.7400.4427.9446.90916456.9454.0642.7424.6406.2393.2307.9389.4396.9400.0423.3439.5$0917456.2470.0480.5486.2483.6475.1462.6449.1430.1431.7436.3438.40918402.7473.1494.7505.5S2-7.9534.452T.9511.3487.0459.0430.3405.01930291.R274.0262.4238.0260.3267.4278.1290.4302.3302.7310.3322.4MEAN OF RATIOS TO SPENCER CURVE.99.99OTD.DEV.7.853EETMEMEOBSEMYVTICNS AND THEIR SUBSTITUTES11190911103.0381.49919303490.0336.900010224201.0300.6A 6iOutputTable 2•3BITUMINOUSCOAt. PROOUCTION100.000 NET TONS1914 —193812 NO8THS MOVING AVERAGE01118GEARJANFEBMARAPRMATJUNEJULYAUGSEPTOCTNOVOEC1914359.3359.5340.0361.2357.6353.4352.0349.3346.8342.0342.1340.919153'1.0340.6340.3341.6346.5356.4367.0374.4389.3399.54G3.G410.01916413.1415.2418.9419.7420.2418.9429.0416.4419.9427.9435.28917443.2449.0453.5455.8458.3460.5480.5455.9458.1458.3462.3465.21910468.8476.0482.1487.0489.9486.8483.6483.6472.7461.0648.0437.31930309.4300.9296.2290.4286.1285.4284.8486.1285.6292.7294.3300.1ICOutput1.63. 2430.04MONTHS MOVING AVERAGE01118.3.0tEARJANFEBMARAPRMAYJUNEJULYAUGSEPTOCTNOVDEC.5.0.4.81914367.3367.7367.7357.0333.5348.2352.2360.0356.9342.3336.0331.06.01915332.0338.0338.2331.7330.2344.2346.7362.2371.0390.0416.0429.21916460.2464.0446.5438.5407.7391.2394.23N1.5390.7405.5486.0430.089.01917448.7463.0473.5486.2487.5481.0471.0453.2438.7437.7437.0430.21918448.2456.2479.0512.2519.5534.2530.1018.5402.0470.0441.3420.21938301.2280.0265.7261.7262.0266.2270.2286.0295.2310.2Output1.63. 28TENTATIVETURNING POINTS. 12 MONTHS MOVING AVERAGETENTATIVE PEAlSDEC083YEAR MOVALUE1419144361.2O531918548N.937919207472.7411319235484.046.051541926 10406.6013719297441.539.5724119341308.438.4828019374383.705.0TENTATIVE TROUGHS08$TEAR MOVALUE22.451519053340.323319169416.436719191403.049919223315.151301924 10390.361671927 11399.972071932 55247.4t24419344296.5925619354300.6102N519387284.8REJECT IONSPEAESTROUGHSMULTIPLE PEAES OR TROuGHS33 19169456.4MULTIPLE PEAES OR TROUGHS236 19384300.6 CyclicalAnalysis of Time SeriesTibI.2-8BITUMINOUS COAL PRODUCTION100.000NET TONS1914 —193801118TENTATIVE TURNING POINTS. SPENCERCURVEBTROUGHSPEAKS19143362.19130331.19186534.19193370.192010486.19226263.19236343.19246377.19271313.192711381.19297464.19326227.19344321.19349279.19371403.19384238.TEST FOR MINIMUM DURATION 0?13MONTHSNOEXCLUSIONST.bI.2-7TURNING POINTS.NMONTHS MOVING AVERAGETROUGHSPEAKS19143368.191412331.19186534.19193372.192011495.19226230.19236549.19247376.19272518.192712376.09296469.19321218.19344326.193410281.193724261.-A 63OutputTaSte2.8BITUMINOUSCOALPROEUCTION100.000 NET TONS1914 —193801118TENTATIVE TURNING POINTS. TINE SERIESTROUGHSPEAKS19143310.191411312.19187550.19193350.192012S38.19224201.192S5568.1924A366.19213565.19211.2310.19295881.19321208.19343363.19349274.19373490.19313252.29143382.0 29141383.0ELIMINATE TURNTEST POR MINIMUM DURATION OP08MINTMSNO EXCLUSIONSFINAL TURNING POINTS. TIME SERIESTROUGHSPEAKS191411312.19187330.19193350.192012338.19224251.19235568.19246366.19273SoS.192712370.19295481.19327208.19383363.19349274.19373490.19383202. 63OutputTaSte2.8BITUMINOUSCOALPROEUCTION100.000 NET TONS1914 —193801118TENTATIVE TURNING POINTS. TINE SERIESTROUGHSPEAKS19143310.191411312.19187550.19193350.192012S38.19224201.192S5568.1924A366.19213565.19211.2310.19295881.19321208.19343363.19349274.19373490.19313252.29143382.0 29141383.0ELIMINATE TURNTEST POR MINIMUM DURATION OP08MINTMSNO EXCLUSIONSFINAL TURNING POINTS. TIME SERIESTROUGHSPEAKS191411312.19187330.19193350.192012338.19224251.19235568.19246366.19273SoS.192712370.19295481.19327208.19383363.19349274.19373490.19383202. 62CyclicalTibI.BITUMINOUS COAL PRODUCTION100.000NET TONS1914 —193801118TENTATIVE TURNING POINTS. SPENCERCURVEBTROUGHSPEAKS19143362.19130331.19186534.19193370.192010486.19226263.19236343.19246377.19271313.192711381.19297464.19326227.19344321.19349279.19371403.19384238.TEST FOR MINIMUM DURATION 0?13MONTHSNOEXCLUSIONST.bI.TURNING POINTS.NMONTHS MOVING AVERAGETROUGHSPEAKS19143368.191412331.19186534.19193372.192011495.19226230.19236549.19247376.19272518.192712376.09296469.19321218.19344326.193410281.193724261.-A 100.000 NET TONS1914 —1938FEBMAR359.3359.5346.8342.0341.6346.5389.3399.5413.1415.2416.4419.9455.8458.3458.1458.3462.3465.2461.0648.0285.6292.7MARAPR367.7367.7344.2346.7416.0429.2446.5438.5486.2487.5438.7437.7437.0448.2456.2261.7262.0TEAR MOVALUE 393.0359.0430.0463.0440.0008.0407.0496.0470.0535.0531.0402.0406.0JAMFEBAPRMAYAUGSEPTMOVDEC057.3334.6341.6336.3332.5331.4332.0383.7400.4427.9446.9642.7424.6262.4238.0260.3302.3302.7 — Selected—July 1953Jan.1951Jan. 1951June 1953June 1953Dec. 1953Aug. 1954Dec. 1953Dec. 1953May 1954 *June1954*Feb.1955Feb. 1955July 1957Nov. 1955Nov. 1955Mar. 1957Mar. 1957Dec. 1957Dec. 1957Apr. 1958Mar. 1958Mar. 1958Apr. 1958Apr. 1958Sept. 1958Sept. 1958May 1960June 1959 *May 1959 *Apr. 1960Apr. 1960Nov. 1960Feb. 1961Jan.1961Jan.1961Feb. 1961Feb. 1961May 1961TNov. 1948Oct.1949July 1953Aug. 1954——5—8——5—8—2—20—1—3—2+2+5+6+2+5+6July 1957—20—20—4—4Apr. 1958—1—100P——j II selectedstrategiclarge.that,Cycle IProgrammedyotldin Shown The These— 3886 Indicators CHARTIndicators11IIIIliiiIIIIIii'iSO44. Business eapenditures, new plant and equipment, 0II-130I0IIIIJ20IIIIIIIII45. Labor cost per unit of output, manufacturing (1957-59 = 1001IiIIhOI1105I-1(00aI-195a*SII-190IIi75aIII46. Labor cost per dollar of real corporate GNP, 0 (1957-59 = 10011(51110II-1105x*-booIIaa-j95aIIIII75IIIIIIIIIIIII(IIIIIIIIIIIIIIIIII1947'50'55'60'65'67 Indicators Coinciding Indicators Indicators CHARTIndicators1IIIIIIIIIIIIIIII60'I30. Employees, nonagricultu.'aI establishments55IC50II51I7570IIIIIII31. Total nonagricultural employmentIIIIIIIIIIIIIIIIIIIIII32. Unemployment rate, totalper cent, inverted scale)aIIIIIIIIIIIIIIIIIIIIIIII1947'50'55'60'65'67 38Cyclical CHARTLeading Indicators 36CyclicalLeading Indicators Leading Indicators 34Leading Indicators DDD5D5D0Leading Indicators33 Leading Indicators— A Burns—A The Burns— pp. Again—A Forproblem,cit., pp. 310 The areA months3.500" tonsMitlion net tonsI1914'16'18'20'28'30'32'34'36Note: The minima -Programmed For AIEutra cyclemeLast of equal.Double turns//ER,JR2Step patternsV2F;Virtual steppatterns withirregularities Per cent20Total Unemployment RateMill6050'II'IIIIIIr'IIIIlxiiI'III1929'35'40'45'50'55'60'65Nonagricultural EmploymentOflS—IIIIIIIIIIIIIIIIIIIII1111111!40309n1929'35'40'45'50'55'60'65 Business Cycles,— 2PROGRAMMED