Forecasting Specific Turning Points

Forecasting Specific Turning PointsAuthor(s): Richard LongSource: Journal of the American Statistical Association, Vol. 65, No. 330 (Jun., 1970), pp. 520-531Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2284564 .

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? Journal of the American Statistical Association June 1970, Volume 65, Number 330

Applications Section

Forecasting Specific Turning Points

RICHARD LONG*

The trade-off between accuracy of the call of a specific turn and the recognition lag is calculated for 17 monthly series from the NBER short list of indicators based on smoothing by Months of Cyclical Dominance (MCD), Average Duration of Run (ADR), and Declining Weights (DW). With a two-month recognition lag and only 1/3 of calls correct, both MCD and DW outperformed ADR. MCD was relatively better for smooth and ADR for irregular series, With each series smoothed to obtain 50 percent likelihood changes are cyclical, the typical leading series led reference peaks by seven months but showed no lead at troughs.

1. INTRODUCTION

In using National Bureau of Economic Research methods for short-term forecasting, the analyst faces several problems not confronted in an historical analysis of economic indicators. First, preliminary data which the practicing forecaster uses may be substantially revised at later dates. Second, even if the preliminary data are not subsequently revised, he must distinguish between cyclical and irregular movements in the time series. Finally, he must decide whether the turning points in the individual series (or specific turning point) herald a coming cyclical change for the economy (a reference turning point) or only a change in the economy's rate of movement.

Nunmerous studies have examined the problem of extra turning points, i.e., specific turning points which did not correspond with reference cycle change [1, 2, 3, 5, 6, 7, 12, 14]. More recently, the effects of data revisions on economic forecasts were investigated [4, 13]. However, how to smooth the data to re- duce the likelihood of mistaking an irregular turn in a series for a cyclical turn and/or reducing the lag in recognizing the specific turning point has remained in the realm of a priori suggestions. Typical is Julius Shiskin's suggestion that series be smoothed by a moving average equal in length to the value of the Months of Cyclical Dominance (MCD) as "a reasonable compromise that avoids many errors of either type" just mentioned [11, p. 534]. Neither the likelihood of calling a false turn nor the length of the recognition lag is specified.

2. DATA AND METHODOLOGY This article will quantify the trade-offs between the recognition lag and the

likelihood of calling a false specific turn for the 17 leading and roughly coincident monthly series included in the 1967 National Bureau short list of indicators [9]. Each of the 17 series will be smoothed by three different methods, detailed

* Richard Long is assistant professor, Department of Economics, Georgia State University. He is grateful to the Federal Reserve Bank of Atlanta for providing encouragement, programming and clerical help for this project while he was on their staff and to the Bureau of Business and Economic Research for supporting completion of the study. The author acknowledges the perceptive comments and suggestions of Rendigs Fels, E. L. Rossidivito, Julius Shiskin and Marshall McMahon on an earlier draft of this article. The author assumes full responsibility for any errors.

520



Forecasting Specific Turning Points 521

in Section 3, for the 1947-63 period. Data have been published for four of the series only since 1948, so 1947 is omitted for those series.' Because a list of specific turns in the post-1963 period has not been published by the National Bureau, 1963 is used as the terminal year. Revised data are used because other studies mentioned earlier treat the problem of data revisions.

Second, all changes of direction in the smoothed series are noted. Next, the recognition lag at each specific turning point is calculated. Since the moving averages are centered, we must count not only the number of months after the turning point when the smoothed series changed directions, but also the future months needed to form the moving average. Thus a 3-month moving average for March requires the unsmoothed data for April. If the specific peak were in January and the smoothed series turned down in March, the lag would be three months. Then we count the number and duration of irregular turns in the

Table 1. LENGTH OF MOVING AVERAGE BASED ON AVERAGE DURATION OF RUN (ADR)

ADR Period of moving average

1.5-1.6 7 1.7-1.8 6 1.9-2.2 5 2.3-2.7 4 2.8-3.2 3 3.3-3.9 2 4.0 or more 1

Source: [101.

series. Finally, summary information is computed for each indicator and for various combinations of indicators.

Some might object to using mechanistic rules for determining specific turning points because they feel that a detailed knowledge of the circumstances causing a change in the direction of an indicator and of the other conditions in the economy must be considered. The author accepts this viewpoint in the practical application of forecasting; but in making judgments about the relative merits of different smoothing devices, it seems legitimate to assume that these other forces will affect all smoothing devices about the same degree.

3. METHODS OF SMOOTHING DATA One of the earlier methods for smoothing economic indicators, suggested by

Geoffrey Moore, is based on the average duration of run of the seasonally adjusted series. The Average Duration of Run (ADR) is the mean number of months the seasonally adjusted series moves in the same direction. The longer the run, the more likely that a change in direction would correspond to a cyclical change. Moore selected a scale, reproduced in Table 1, in which the number of months used to smooth the data is a function of the ADR of the original series. A series so smoothed would have an ADR of about five months [8, 10].

1 Specific turns not corresponding to a particular reference cycle are included. The dates of these extra turns were supplied by the National Bureau of Economic Research.



522 Journal of the American Statistical Association, June 1970

The Months of Cyclical Dominance (MCD) is the number of months it takes the mean absolute percentage change in the cyclical factor (C) to dominate the mnean absolute percentage change in the irregular factor (7). The magnitude of the irregular factor remains about the same regardless of the time span, but the cyclical amplitude cumulates as the span increases. Choos- ing one for the critical value of 7/Z is based on "the idea that it yields a series dominated on the average, by the cyclical rather than the irregular factor, with the smallest loss of current figures" [11, p. 543].

In the third smoothing device tested in this study, S. S. Alexander utilized arithmetically declining weights (DW) as follows: Zt=1/14(5Xt+4Xt_j +3Xt_2+2Xt-4+Xt-3-Xt_6) He noted this formula has properties similar to that of a second degree polynomial fit to each set of seven successive observations with the smoothed value corresponding to the next to last observation. Such a curve would preserve curvilinearity which an equally weighted moving average would smooth. He also claimed this formula would result in a shorter recognition lag at turning points than an equally weighted moving average of comparable smoothing power [1].

Two other smoothing devices were considered, but not used here. Ashley Wright proposed fitting a trend line to past observations of a series and determining confidence limits two standard errors from the trend line. If an expanding series fell below the lower confidence interval, a peak was declared to have occurred in the series. An analogous method was used for determining troughs. This method has been partially tested with poor results [6, Chap. 3]. Wright's method is somewhat ambiguous on the number of past observations to which the trend line should be fitted. Confidence intervals based on functions fitted to time series data are biased because of serial collinearity. Finally, the fitting of trend lines to each series at every turning point might preclude its widespread use even if successful.

A fifth formula used by Herman Steckler is Zt = 1/4Xt+3/4Zt- [5, 12, 14, 15]. The average lag for this smoothing formula of three months-the same average lag as a six-month equally weighted average-is rather large compared with other smoothing formulas. Moreover, the likelihood of calling a false turn was about 80 percent for the diffusion index of the industrial production index even with the large lag [5 ]. The three-month average lag implies a four-month recognition lag because an extra month is needed to observe the change in direction.

Of the three smoothing devices tested, the ADR and MCD criteria use different moving averages for series differing in smoothness, but Alexander's declining weights formula uses the same formula for all series.

4. THE RESULTS

Table 2 gives the accuracy score based on both the criterion of any change in direction of the smoothed series and that of only counting changes in direction persisting two or more months. This facilitates comparisons with other smoothing devices having a recognition lag about a month longer. Thus, one could require a two-month signal (which would lengthen the recognition lag by a month) and then compare the accuracy scores. Since there is little variance



Forecasting Speciflc Turning Points 523

Table 2. SUMMARY MEASURES OF RECOGNITION LAG AND ACCURACY: 17 LEADING AND ROUGHLY COINCIDENT SERIES

FROM NBER SHORT LIST

Mean recognition lage Percent of true turns to Turn and type of series (months) true and false turnsb

MCD ADR DW MCD ADR DW

All specific turns 11 Leading series 2.2 3.6 2.0 34; 48 53; 61 37; 54 6 Roughly coincident series 1.5 2.6 2.2 28; 47 44; 55 42; 58

Total 2.0 3.3 2.1 32; 47 50; 59 39; 56

All specific peaks 11 Leading series 2.0 3.5 1.9 33;48 51;58 34;55 6 Roughly coincident series 1.5 2.7 2.3 20;37 33;42 31;44

Total 1.8 3.2 2.5 27; 44 43; 51 33; 51

All specific troughs 11 Leading series 2.2 3.7 2.1 35;48 54;65 41;54 6 Roughly coincident series 1.5 2.4 2.0 51; 64 68; 82 66; 85

Total 2.0 3.3 2.1 39; 52 58; 70 46; 61

a Lag with a one-month signal. The lag with a required two-consecutive-month signal would be one month longer.

b The figure following the semicolon is the accuracy figure when a two-consecutive-month signal is required for calling a turn.

among accuracy scores for changes in direction lasting three or more months, they are not tabled.

The recognition lag assumes a zero month publication lag. The publication lag varies from about zero for stock prices to about two months for changes in business inventories. In comparing alternative smoothing formulas, the publication lag need not be considered. However, to judge the usefulness of the indicators one must consider the lead of the series, the recognition lag (including data gathering and publication lags), and the accuracy of the "recognition," as well as the uses the knowledge of specific turns affords.

Note that the accuracy scores are based on cases in which the smoothed series changed directions. If cases in which the smoothed series did not change directions were included in the denominator, the accuracy scores would be considerably higher. For all series at peaks and troughs, the measures for MCD, ADR, and DW formulas, respectively, would be 91, 96, and 93 percent. For purposes of identifying specific turning points, the more relevant measure is that which considers the ratio of true signals to all changes in direction of the smoothed series. If the alternative were used, one would have to decide how to treat cases in which the smoothed series continued in the same direction even though a specific turning point had occurred.

For all specific turning points, the MCD smoothing method resulted in not only the shortest mean recognition lag (2.0 months) but also the highest likelihood of a change in direction being irregular in natures-only 32 percent of the signals were correct. The seven-term declining weights formula gave a slightly longer recognition lag (2.1 months) but a higher accuracy (39 percent). The




ADR formula had a long recognition lag (3.3 months) but was least likely to signal a turn falsely (50 percent). However, if one adopted the DW method and required the smoothed series to continue the change in direction two months before considering the change cyclically significant, the lag becomes 3.1 months and the percent of total true signals, 56 percent. In this case, the DW method outperforms the ADR method on both measures. Thus, the relevant choice is between the MCD criterion with 0.1 month shorter recognition lag and the DW formula with a seven percentage point smaller chance of giving a false signal.

For leading series, the DW criterion is best; but for roughly coincident indicators, the 0.7 month better recognition lag for MCD must be weighed against the 14 percentage point better accuracy for the DW criterion. At peaks, for all series, DW criterion had a six-point better accuracy but a 0.3 month longer recognition lag. At troughs, MCD has a shorter mean recognition lag, but DW is seven points more accurate.

Since the ADR method generally had a recognition lag more than one month greater than alternative methods and the accuracy of the ADR method was not better than an alternative which used a rule for a two consecutive month signal for an indication of cyclical significance, the ADR method must be judged inferior. The failure of the ADR criterion results from its long moving average. For the 17 leading and roughly coincident series, the mean ADR moving average was 4.4 months-1.8 months longer than that for the MCD method. In addition, more of the ADR moving averages were even numbered, a point to be expanded later.

For the MCD criterion, the mean moving averages for the more erratic leading series is 0.9 months longer than for the roughly coincident series. The corresponding difference in the means for the ADR method is 1.3 months. Ap- parently, an oversmoothing is performed in the leading series relative to the coincident series because the percentage of false signals is greater for the coincident series under both smoothing procedures. The declining weights method, which used the same smoothing formula for each series, indicates that the leading series are still more erratic than the coincident series given the same degree of smoothing.

Summary measures for individual indicators based on the MCD and ADR criteria, similar to the measures for groups of indicators in Table 2, are given in Table 3. Because of the overall poor performance of the ADR criterion, detailed data are not given for it.

In examining Table 3, the reader may wonder why the recognition lag is less than one month for industrial production and less than the extra number of months needed to form the moving average for some other series. This results partly from the National Bureau's conservative choice of turning points. In cases of doubt between two alternative dates, the latter date is chosen. For example, the values for industrial production from December 1960 through April 1961, inclusive, were 103.0, 103.6, 103.6, 104.0, and 106.7. The NBER dated the trough in February, presumably because no increase occurred between January and February. Since the recognition rule used here assumes that a series con- tinues in the same direction, then, if a series did not change from the preceding




Table 3. RECOGNITION LAG AND ACCURACY OF SERIES SMOOTHED BY MCD MOVING AVERAGES AND DW FORMULAS

Accuracy (%) BCD Series (MCD) Peak or Recognition lag no.

Series (MCD) trough (months) 1 month 2 months

MCD DW MCD DW MCD DW

Leading series

1 Avg. wkly. hours, mfg. (3) P 0.7 1.0 27 25 30 33 T 2.5 2.0 40 57 50 57

4 Nonagr. placements (2) P 1.8 1.6 83 56 83 83 T 2.6 1.8 29 36 31 42

6 New orders, dur. mfg. (3) P 1.8 2.2 31 31 63 56 T 2.4 2.4 42 38 50 63

10 Contracts and orders, P 2.5 2.3 31 31 50 57 plant and equip. (4) T 4.0 3.0 40 31 40 40

12 Net business formation (2) P 2.0 2.7 30 38 33 43 T 1.5 1.5 50 67 80 80

17 Price per unit labor P 1.8 2.0 33 36 40 40 cost (3) T 2.3 2.3 33 31 40 40

19 Stock prices, S & P (2) P 2.2 2.2 36 50 42 71 T 2.2 2.2 45 50 56 63

23 Indus. material prices (2) P 2.0 1.8 45 63 50 83 T 2.4 2.4 33 45 38 63

29 Housing permits (3) P 1.2 1.4 31 45 56 71 T 2.2 2.6 28 33 63 45

31 Change, bk. val. P 3.0 1.8 20 15 44 40 inventories (5) T 3.8 2.4 33 50 63 83

113 Change, consumer P 2.4 2.2 28 33 50 50 install. debt (3) T 1.2 2.0 31 38 50 56

Roughly coincident series 41 Nonfarm employment (5) P 1.0 2.3 21 40 100 50

T 1.0 2.5 40 80 44 100 43 Unemployment rate (2) P 2.0 2.8 29 31 29 36

T 2.5 2.0 67 67 67 67 47 Industrial production (1) P 1.0 1.8 17 36 36 40

T 0.5 1.8 50 67 67 67 52 Personal income (1) P 1.0 2.3 13 43 50 75

T 1.3 1.3 43 100 100 100 54 Retail sales (2) P 1.7 2.0 14 14 23 25

T 0.7 1.0 75 60 75 100 56 Mfg. and trade sales (2) P 2.4 2.8 33 42 35 71

T 2.6 2.8 50 50 63 100

month, the recognition date was counted as January. This gave a recognition lag of -1 month relative to the NBER trough date of February.

In other cases, when the formation of the moving average may have unex- pected effects, such as a period of small upward changes followed by a sharp drop in the series, the month in the smoothed series includes this sharply declining value (even though not centered on that month), and the moving average declines.

Finally consider the data beginning in August 1952, which peaked in March 1953, shown in Table 4 (decimal point omitted). The moving average declined




Table 4. UNSMOOTHED AND SMOOTHED DATA FOR AVERAGE WEEKLY HOURS, MANUFACTURING AUGUST 1952-MARCH 1 953a

Date

Data Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May

Unsmoothed 405 411 411 410 411 410 409 411 410 409 3-mo. avg. 406 409 411 411 410 410 410 410 410 409

a Source: Bureau of Labor Statistics.

in December and was recognized when January data permitted the formation of the centered December moving average. Here the recognition lag was -2 months.

In developing the average duration of run and months of cyclical dominance criteria for moving averages, Geoffrey Moore and Julius Shiskin thought of the procedure as one giving equal degrees of smoothness to all series. Though this may be good for historical analysis, when the number of months is even and the series is centered, this procedure can be costly to the practicing forecaster. Eight of the 17 best conforming leading and roughly coincident indicators have an even numbered MCD value. For the ADR criterion, 13 of the 17 are smoothed by an even number of months. The disadvantage of such a procedure is that it "throws away" one-half of the information for the most current month if the moving average is centered.

For example, the formula for a two-month moving average is Zt 1 1/2(0.5Xt+1+Xt+0.5Xt_1) i.e., the most current month is given only one-

half the weight of other months except the earliest month in the average. From a data availability viewpoint, one could just as quickly (even more quickly in terms of computational time) compute a three-month moving average, Zt = 1/3(Xt+?+Xt+Xt-1). In the odd-numbered, centered moving average, all months are given equal weight. The comparative results for using an odd- numbered versus an even-numbered moving average for both the MCD and the ADR criterion are given in Table 5 for those series in which MCD and ADR are even, respectively.

Though the paired results are not different in a statistical sense, even if one assumes normality and paired observations, the easier calculation of an odd valued average and the heavier weight given to the most recent observation would seem to argue for using odd-valued moving averages. This argument

Table 5. COMPARISON OF SERIES SMOOTHED BY BOTH EVEN AND ODD NUMBER OF MONTHS

Recognition lag Accuracy (%) Smoothing criterion Series (eontia- (mont hs) 1 month 2 months

Even-valued MCD 8 2.1 37 44 MCD+1 8 2.0 37 59 Even-valued ADR 13 3.3 52 61 ADR+1 13 3.1 48 64




seems particularly applicable to the number of series where the maximum MCD is defined as 6. I would prefer making the maximum MCD equal to 7 since no loss of currency is involved in using the longer average, and the charted series looks slightly smoother. Out of 84 monthly series for which MCD values are listed in Business Conditions Digest, 41 had even-valued M\CD's, and seven series had an MCD equal to six months.

Overall the performance of the MCD criterion and the DW formula are roughly equivalent (Table 2). Since the MCD criterion uses different length formulas for series differing in smoothness while the DW formula does not, examining the two formulas according to the smoothness of the series seems appropriate. When MCD is 1 or 2, the MCD smoothing device gives a much smaller recognition lag while the accuracy of the DW is considerably higher. For MCD = 1, the MCD criterion is better than the DW criterion. That is, when MCD equals 1, one could require a two-consecutive month signal that would give a mean recognition lag of 1.6 months and an accuracy of 56 percent. The comparable figures for a one-month signal with the DW formula are 2.0 months and 52 percent. For larger values of MCD (4 or 5 months), the mean recognition lag is smaller for the DW formula, and the accuracy scores are about equal. Thus, it appears relatively more advantageous to use the MCD moving average when the MCD value is small and the DW formula when MCD takes a high value. Though these results agree with a priori expectations (that the DW formula would be relatively better on more erratic series), the small sample size can give only very tentative conclusions. For details, see Table 6.

Since the MICD smoothing method outperforms the DW method for less irregular series and the DW formula is invariant with respect to the smoothness of the series, it might be possible to improve the DW performance by using a formula with a shorter lag (and less smoothing power). Rendigs Fels suggested one possibility: Z= 1/9(4Xt+3Xt-1+2Xt-2+Xt-3-XtX5). Such a formula would have an "average lag" of 0.6 months compared with 1.0 months for the formula used in this study [15]. Alexander chose weights such that the average lag would equal exactly one month, so the smoothed series could be centered.

In setting up their explicit scoring system for indicators, Shiskin and Moore scored the monthly series for smoothness by: S = 120-20 MCD, where S equals

Table 6. RECOGNITION LAG AND ACCURACY SCORES CLASSIFIED BY MONTHS OF CYCLICAL DOMINANCE

Mean 1 and 2 month MCD Series recognition lag accuracy signals

MCD DW MCD DW

1 3 1.0 2.0 24;56 52;63 2 7 2.0 2.2 37;46 43;59 3 5 1.9 2.0 32;48 36;50 4 1 3.3 2.6 33;44 31;47 5 1 3.4 2.1 26;53 24;56

Total 17 2.0 2.1 32;47 39;56




the smoothness score. Thus a series with an MCD of 1 would get a value of 100, and a series with an MCD of 6 would get a score of zero [9, Appendix A]. Though the relative smoothness scores proposed by Moore and Shiskin generally agree with the results here, this is not universally true. For example, the net change in consumer installment debt with an MCD of 3 has a recognition lag of 1.8 months and an accuracy score based on a one- and a two-month change in direction, respectively, of 29 and 50 percent. The comparable scores of manufacturing and trade sales with MCD equal to 2 months-2.5 month recognition lag and accuracy of 40 and 45 percent-are probably worse than those of the change in consumer installment debt. The difference between my scores and the MCD values, relatively, may reflect the proportionately higher 7/Ci ratio occurring in the vicinity of specific turning points for manufacturers and trade sales than for the total period.

The number of months for cyclical dominance is defined as the span of months it takes the mean absolute percentage change in the cyclical component of the series to exceed the mean absolute percentage change in the irregular component for the same span. (If the fraction does not equal an integer, the MCD is rounded to the next highest integer). Thus it would appear that a change in an MICD series would have a less than 50-50 chance of registering a false signal of a cyclical change. Yet, for the 17 series tested, the frequency of false signals was 68 percent. The difference results from the tendency of cyclical changes to become weaker in the vicinity of turning points (expansionary and contractionary forces are roughly equal) and of irregular movements to become more pronounced around turning points.

For example, in the retail sales series used to illustrate the X-11 seasonal adjustment program [16], C equaled 0.42 and 7 equaled 0.85, on the percentage changes from the preceding month. Using the same data, but computing C and I only for those periods within ? 6 months of the specific turning points gave values of 0.30 and 0.94, respectively. Thus for the total period the 7/C is 2.03, while for the period around specific turning points the 7/C is 3.08 or about 50 percent larger. Because of these differences, it would be helpful for the analyst to know the 7/C ratio, not only for the total series but also for the period close to the specific turning points. If the differences in the ratios for retail sales are typical, perhaps the figure 1.5 instead of 1.0 would be more appropriate for the months of cyclical dominance.

The reader may think that the size of the recognition lag and the publication or reporting lag negates the usefulness of the indicators. However, at least with respect to reference cycle peaks where a 7-month lead still prevails, that is not the case. In Table 7, the shortest possible recognition lag is chosen, given that the accuracy of the called specific turn must be at least 50 percent. For each series, at both peaks and troughs, the smoothing device and the number of months the signal must continue to realize a 50 percent accuracy are given. To this lag is added the reporting lag for Business Conditions Digest (BCD) for each series to obtain the total lag. The total lag is then added to the median lead or lag of each series to obtain the "typical" time the forecaster expects to recognize the specific turning point relative to the reference cycle turn. If one wanted to shorten the lag, he could watch the financial press and obtain




Table 7. TOTAL RECOGNITION LAG AND MEDIAN LEAD

Peak .. Median Total lag BD eio Release Report- Smoothing No. of Recogni- Total l edian BCD Series or date" ing lagb method signals8 tion lag lag lead +median

Leading series 1 Avg. wkly. hours, P 8th 1 MCD 3 2.7 3.7 -6 -2

mfg. T 1 DW 1 2.0 3.0 -4 -1 4 Nonagria. placements P 15th 1 MCD 1 1.8 2.8 -11 -8

T 1 DW 2 3.8 4.8 -1 +4 6 New orders, dur. mfg. P 21std 1 MCD 2 2.8 3.8 -8 -4

T 1 DW 2 3.4 4.4 -2 +2 10 Contraats and orders, P BCDe 1 ADR 1 3.5 4.5 -8 -3

plant and equip. T 1 DW 3 5.0 6.0 -3 +3 12 Net business formation P BCDe 2 MCD 3 4.0 6.0 -20 +4

T 2 DW 1 1.5 3.5 -3 +1 17 Price per unit labor P BCDe 1 MCD 4 4.8 5.8 -11 -5

cost T 1 MCDf 3f 4.3 5.3 -3 +2 19 Stock prices, S &P P 1st 1 DW 1 2.2 3.2 -4 -1

T 1 DW 1 2.2 3.2 -4 -1 23 Indus. material prices P 4th 1 DW 1 1.8 2.8 -6 -3

T 1 ADR 1 3.2 4.2 0 +4 29 Housing permits P 15th 1 DW 2 2.4 3.4 -13 -9

T 1 ADR 1 3.0 4.0 -5 -1 31 Change, bk. val. P 5th+ 2 DW 3 3.8 5.8 -14 -8

inventories T mo. 2 DW 1 2.4 4.4 -6 -2 113 Change, consumer P 5th+ 2 DW 2 3.2 5.2 -12 -7

install. debt. T mo. 2 MCD 1 1.5 3.5 -4 0 - 11 Leadingseries P - 1.3 - - 3.0 4.3 -11 -7

T - 1.3 - - 2.9 4.2 -4 0

Roughly coincident series

41 Nonfarm employment P 8th 1 MCD 2 2.0 3.0 -2 +1 T 1 ADR 1 2.0 3.0 0 +3

43 Unemployment rate P 8th 1 ADR 3 5.3 6.3 -4 +2 T 1 DW 1 2.0 3.0 +2 +5

47 Industrial production P 17th 1 DW 3 3.8 4.8 0 +5 T 1 MCD 1 0.5 1.5 0 +2

52 Personal income P 20th 1 MCD 2 2.0 3.0 +1 +4 T 1 DW 1 1.3 2.3 -2 0

54 Retail sales P 5th 1 DW 3 4.0 5.0 +1 +6 T 1 MCD 1 0.7 1.7 0 +2

56 Mfg. and trade sales P 5th+ 2 ADR 1 3.4 5.4 -4 +1 T mo. 2 DW 1 2.0 4.0 0 +4

- 6 R. C. series P - 1.2 - - 3.4 4.6 -1 +4 T - 1.2 - - 1.4 2.6 0 +3

- 17 Series P - 1.2 - - 3.1 4.3 -6 -2 T - 1.2 - - 2.4 3.6 -2 +2

a Typical date the issuing agency releases the statistics after the month of reference. If i +mo." appears, it is the date two months after the month of reference.

b Reporting lag compares latest data reported with issue date of BCD. If June data is the latest reported in the July issue, the lag is one month.

c Number of months the signal must continue, so the accuracy score will be 50%. d Advance release; regular release appears on the 5th of the following month. e Data released only in BCD which is issued about the 30th of the month. f ADR with a 2-month signal gives the same results.

the data the day after release by the issuing agency, (for the typical reporting lag for this source, see Table 7, Column 4). Since this would only be feasible for someone spending considerable time watching the indicators, the total lag is based on the use of BCD alone.

Note that though overall the ADR smoothing method fared badly, for a few indicators it gave the shortest recognition lag consistent with a 50 percent ac-




curacy. For the roughly coincident indicators, the four- and three-month identification lag is consistent with the lags in recognizing cyclical turning points established in several recent studies.

5. CONCLUSIONS

1. It is possible to quantify the trade off between the recognition lag and the accuracy of the prediction of specific turning points. This information will pro- vide the practicing forecaster a better idea of his conclusions' reliability. More- over, as additional information accumulates, such as continuation of a new trend in a series for another month, he can see how this improves the odds of the trend being cyclical in nature.

2. The shift from using moving averages based on the average duration of run to those based on months of cyclical dominance with the introduction of the Census II seasonal adjustment procedure in the late 1950's appears to have been a wise trade off in that the much shorter recognition lag more than offsets the lessened accuracy of the signal.

3. Using the MCD moving averages results in irregular changes about two times out of every three changes in direction, so that, in practice, the cyclical factor on an average does not dominate the irregular factor for changes in the smoothed series.

4. If the moving average is even numbered, the forecaster would likely do a little better by smoothing the series by the next highest (odd) number of months or not centering the smoothed series. This argument is based primarily on a priori grounds since the empirical results for the odd-numbered moving average were only slightly (and statistically, nonsignificantly) higher.

5. The measures of I and C would be improved if we knew their values in the vicinity of turning points as well as for the total period.

6. The DW formula which seems only to have been used in journal articles, would be a useful addition to the forecasters' tool bag, particularly for irregular series.

7. A comnparison of the recognition lag, publication lag, and median leads for the leading series suggests that, typically, these series still have a seven month lead relative to reference peaks, but no lead relative to troughs if one is willing to accept a 50-50 chance the specific turns are called correctly.

REFERENCES [1] Alexander, Sidney S. and Stekler, Herman O., "Forecasting Industrial Production,

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[51 Dyckman, T. R. and Stekler, Herman O., "Probabilistic Turning Point Forecast," Re- view of Economics and Statistics, 48, No. 3 (1966), 288-95.




[6] Long, C. Richard, "An Evaluation of Ashley Wright's Forecasting Method," Unpub- lished Ph.D. dissertation, Vanderbilt University, 1968.

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[8] Moore, Geoffrey H., "Diffusion Indexes, Rates of Change and Forecasting," in Geoffrey H. Moore, ed., Business Cycle Indicators, New York: National Bureau of Economic Research, 1961.

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[13] and Burch, Susan W., "Selected Economic Data, Accuracy Versus Report Speed," Journal of the American Statistical Association, 63 (June 1968), 436-44.

[14] , "A Simulation of the Forecasting Performance of the Diffusion Index," Journal of Business, 35, No. 2 (1962), 196-200.

[15] , "On Smoothing and Lags," American Statistician, 14 (December 1960), 13. [16] U. S. Bureau of the Census, "The X-11 Variant of the Census Method II Seasonal

Adjustment Program," Technical Paper No. 15, Washington, D.C.: U. S. Government Printing Office, 1965.



Forecasting Specific Turning Points

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