at any given time we can find trend lines which are both up and down. Refer back to Figure III-5 for example. We know from the manner in which this chart was constructed that if the chart were continued longer than shown we could draw another channel using the peaks and lows of component "C" of Figure III-2. This channel is strictly an upside channel, and the bottom bound of it forms strictly an uptrend ne-during the precise time period when the trend lines of Figure JII-5 are both up and down!

So Which of These Has What Meaning?

Exactly the same is true of all other chart patterns. We will often find, for example, that the left shoulder (or head, or right shoulder) of a clearly visible head and shoulder pattern will exhibit a head and Shoulder pattern of its own. This is, of course, caused by shorter-term cyclic fluctuations than those which formed the larger pattern. But again, the chartist usually sees only one of these, and appears at a loss to explain the significance of more than one when they appear.

On What Basis Does He Attach Significance to One and Not to the Other?

Triangles, flags, etc., marked by a chartist may also be seen to form only a part of a larger triangle or flag. Why did the chartist single out the one he did for detailed consideration? This is all considered to be a part of the "arty" aspect of charting. Actually, the missing link is knowledge of cychcality. The trouble is that there is no reference time period on which to base a selection. And even if there were, this reference tune period would have to be different depending on whether daily, weekly, monthly, or yearly charts were considered!

Our cyclic model neatly solves this dilemma. For the facts are that all such patterns within patterns are significant. The cyclic model, by providing the explanation for chart pattern formation and the relationship between magnitude and duration of components, essentially quantifies the significance of each chart pattern that forms. This is what we are evaluating in effect by our tables which show the up-down-sidewise status of each observable periodicity. We not only see when members of these are working together to produce price motion in either direction, but we can predict when the pressures of each are likely to let up. In cases of nip and tuck, we can then call into play our knowledge as to how much more potent any one component is than, say, two others that may be opposing it-based upon our knowledge of magnitude vs. duration. We can further refine our estimates as to what is likely to happen by noting signs of magnitude-duration fluctuation in each component by observing the formation of flags, failure to fill constant-width envelopes, etc. By adding knowledge of cyclicality to charting technkiues we take a major step in reducing the "art" of charting to the "science" of prediction!

THE SIGNIFICANCE OF MOVING AVERAGES

Now lets discuss an artificial chart pattern. As we have seen, the price motion of stocks forms repeating patterns for perfectly valid cyclic reasons. However, the chartist

has s more in the way of tricks up liis sleeve. As you otserve chart services, you will often note the addition of curving lines to the chart which appear to be somewhat related to price motion, but are not a part of it. These are "moving average" lines, which have come into popular usage quite recently. Why are these added to the chart and of what significance are they? Each of these has been tested by usage and found to convey more information than if price action alone were displayed. In short, they were derived empirically (which means stumbled upon more or less by accident!), and found to be of some use.

In order to understand why these are useful, we must probe deeply into what the characteristics of a moving average consist of This is done in the Appendix, and only the significant results are presented here.

1. A moving average is a "smoother." It is a numerical process applied to a sequence of numbers (such as the time sequence of closing prices of a stock). The result is an elimination or reduction in magnitude of short-term fluctuations, while leaving the longer-term fluctuations modified Uttle if at all. The net resuh is a smoother time sequence of numbers than the sequence to which it is applied.

2. But there is a variable involved in the use of a moving average. For example, the most commonly used ones are a ten-week and a 30-week moving average. This simply means that in each case the average is formed over a ten-week time span, or over a 30-week time span. By inspection of the results it can be seen at once that they are different (Figure III-l 0). Yet they operate upon the same numbers, namely the closing prices of a stock. Obviously, the time span of the average used alters its characteristics.

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Moving Averages Versus Time-Span

3. These alterations in characteristics can be completely quantified and predicted (as in the Appendix). The following general results are found to be true:

a) A moving average of any given time span exactly reduces the magnitude of fluctuations of duration equal to that time span to zero.

b) The same moving average also greatly reduces (but does not necessarily eUminate) the magnitude of all fluctuations of duration less than the time span of the moving average.

c) All fluctuations of greater than the time span of the average "come through," or are also present in the resulting moving average line. Those with durations just a little greater than the span of the average are greatly reduced in magnitude, but this effect lessens as periodicity duration increases. Very long duration periodicities come through nearly unscathed.

4. Notice that the "cutoff point, or point where a given duration periodicity is completely eliminated (duration equal to the span of the average), is a controllable variable. By choosing the span of a moving average correctly, we can control this cutoff point, thus controlhng what duration periodicities we want to suppress, or want to allow to come through for observation!

From the above description of a moving average it is seen right away that the user, while not necessarily possessing knowledge of cychcality in price motion, nevertheless is employing a tool which is only useful in accentuating or diminishing visibility of cycUcality. That the result does indeed produce enough useful results to warrant a great deal of extra computational effort in stock charting is a tribute and testimony to the significance of cyclic phenomena in stock price motion!

WHY TEN-AND 30-WEEK MOVING AVERAGES ARE USEFUL

Now then. Why should empirical results have shovm the ten-week and 30-week moving averages to be exceptionally useful? Is this explainable in terms of our model?

Refer back now to our cyclic model component tabulation of Chapter Two. Remembering the significance of the moving average time span in setting a smoothing "cutoff point in fluctuation duration, we note that a ten-week span moving average will set a cutoff point almost exactly midway between our 6.5- and 13.0-week duration components. This means that all components of 13.0 weeks duration and more wiU show up in the moving average results, while the components of 6.5 weeks and less will be drastically reduced in magnitude (or "smoothed" out). Well! We find that a ten-week moving average is useful because it calls our attention only to cyclic fluctuations of 13 weeks and longer, allowing us to ignore the "distracting" shorter duration oscillations.

What about a 30-week moving average? The cutoff this time is found to be between the 26-week and nine-month (39-week) components of our model. This time, all cychc phenomena of nine months or longer duration are allowed to "come through" while components of duration 26 weeks and less are ignored or smoothed! In other words, if we had set up these smoothing objectives in advance with full knowledge of the importance of our cyclic model in mind we could not have chosen the proper "cutoff points much better-right smack in between the nominal durations