of several of our most interesting and dominant cyclic components! It seems that once apin our chartists are very observant people. Without full awareness of cyclic phenomena, they nevertheless used trial and error methods to good avail and came up with the right answers.

HOW TO PLOT AND INTERPRET A MOVING AVERAGE PROPERLY

There is, however, one small but important characteristic of a moving average which they did overlook. This is demonstrated in the Appendix, and described here.

A moving average is an effective smoother of fluctuatir time sequences of data. However, the time relationship between the moving averse and the data it smoothes is not the one that is always shown on stock price charts. In fact, the moving average data point plotted in association with the last price datum should be associated with a price datum one-half the time span of the average in the past!

Lets make this clearer with an example. Suppose were computing the latest possible moving average data pomt for a ten-week moving average of the weekly closing price of a stock. The procedure used is to add up the last ten weekly closing prices, then divide the sum by ten. Now on stock price charts, the resulting value of the ten-week moving average is always plotted at the time of the last price data point used in computing the average. This is incorrect!

The proper time relationship between the computed moving average and the stock price data it is smoothing is obtained by plotting the value computed above at a time half-way between the fifth and the sixth previous price data points. This falls in the middle of the week of a weekly chart, and hence is associated with no value for the weekly close of the stock. For this reason, it is always better to use an odd number of data points in preparing a moving average, so that there is always a stock price to be associated with each average datum computed.

HOW A MOVING AVERAGE CAN AID CYCLIC ANALYSIS

What does all of this mean? Well, it can be important. Take a look at Figure III-l 1. The weekly data for Alloys Unlimited (as used in Figure III-l 0) is presented. On this chart the ten-week moving average of Figure III-l0 has been shifted five and a half weeks into the past as it should property be plotted. is now apparent that this line represents a smoothing of actual price fluctuations. In fact, it is found to move almost precisely down the center of one of our now famiUar constant-width channels!

What is happening? Remember that the ten-week moving average is suppressing all fluctuations of less than ten weeks duration while allowing longer duration periodicities to "show through." In this case, the ten-week moving average is an imperfect (but not bad) representation of the sum of the 13-week and all longer duration periodicifies! The 13-week cycle here just barely comes through (note the dip in the moving average at the top of the peak in May-June). However, the longer 24-week component (equivalent of the 18- to 20-week cycle of the model), and all longer duration fluctuations are tracked to perfection. Note the difference in visibility achieved by this means as you compare Figures lU-l0 and III-11!

ALLOYS UNLIMITED

TIME-SHIFTED

WK. MOVING AVCRAOE-

1968

; FIGURE HI

/ ; ;

/ CONSWIT WIDTH -ENVELOPE

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Xentering" A Moving Average

When plotted in this correct manner, two immediate uses for a moving average come to mind:

1. It can be used to help isolate any desired component. By selecting the span of the average properly, the stock price can be caused to oscillate about the moving average in sympathy with the shortest duration component that the average does not suppress! With this added visibility, we can often then pla(» the conect envelope about cyclicality, unambiguously selecting the proper highs and lows.

2, Since the moving average (plotted in this manner) only faib to be "up-to-date" by about one-half the duration of the component isolated above, we can usually estimate quite accurately (from the remaining stock price motion) what the average will later be shown to be doing-hence the envelope also.

These techniques can be of considerable help in the case of some stocks where, for one reason or another, cyclicality is not readily apparent.

Here is a case then, of an artificial price motion pattern which the chartist has found from experience to be useful. Its utility is seen to be directly explainable in terms of the "X motivation" model. Even more important, understanding of the model and of the characteristics of moving averages allows us to utilize the moving average properly, and in ways not yet exploited by chartists at all!

SUMMARIZING CHART PATTERNS

It is time to sum up the results of this chapter. We could go on and on comparing the expectations of the cyclic model with chartist observations-and this has been done

in extensive detail. In every case the model is shown not to be m conflict with charting principles. Instead, it explains chart pattern existence and formation, and provides the applicant with interpretation and information not otherwise available.

As you continue reading, you should keep in mind at all times the following relationships between cyclic analysis and chart patterns:

1. Chart patterns form and repeat because of the repetitive nature of cyclic price action.

2. Trend lines and channels are a mandatory outprowth of the price-motion model.

3. Head and shoulder, double tops and bottoms, and "V" chart patterns are all caused by the same cyclic action. Whether one or the other results is completely dependent on the time relationships of the cycUc components that cause the pattern.

4. Triangles, diamonds, wedges, flags, and pennants are formed by the same type of cyclic action. In these patterns, the magnitude-duration fluctuation aspect of the price-motion model is dominant. Triangles may also be formed by a similar process to that which produces head and shoulder type patterns. It is essential for you to be able to differentiate between the two formative causes.

5. Cyclic analysis provides the means of telling in advance in which direction prices will go when a pattern terminates.

6. The price-motion model provides the reference times without which chart pattern analysis remains an "art."

7. Moving averages are smoothers.

8. The "span" of a moving average is the lissign vnriable that ofrmits the use of such averages to improve cyclic visibility.

9. The price-motion modei explains the signitlcance of the empirically derived ten-and 30-week moving averages.

10. A moving average becomes a great deal more useful if properly plotted. To do so, the theoretical time lag of such an average must be taken into account.

11. Moving averages can be of aid in cycl-. analysis. They can be used to establish the trend of summed long-duration cyclic components, and to identify unambiguously lows and highs about which curvilinear channels should be formed.