Nothing is perfect-there are pitfalls.

Cyclic analysis can be wrong due to transient fundamental factors, magnitude-duration fluctuation, and overlooked long-term components. Trailing loss levels will protect you in most cases.

The most important antidote for psychological barriers is awareness of their existence and importance.

Outside influences, however well meant, can upset the statistical balance of things for you.

Greed is a problem. Use knowledge of the effectiveness of profit compounding to counteract it.

A stock seldom appears interesting at the ideal time to buy. It usually looks too good to be true when its time to sell.

There is a psychological effect attributable to chart time vs. real time. When using charts, scale factors are important.

You must train yourself emotionally to sell into rising markets and buy into falling ones.

Howefver, regardless of whether or not this is a vaUd explanation of why, it is certainly a fact that people in general do not get more and more in the mood to buy stocks as prices go down. Conversely, the mood to sell does not strike harder and harder as prices rise. Yet the exact opposite of this mood is absolutely mandatory if we are to "buy low and sell high," and this is precisely what we must do in order to profit in the market.

Therefore, if we condition ourselves to behave as though something is cyclically causing our emotional outlook to vary (which in turn causes us to be bearish or bulli at the wrong times), and if we consciously try to combat the assumed forces, we will find ourselves doing all the right things: i.e., being in a frame of mind Xasell into rising markets and buy into falling markets. This alone cannot guarantee us profits, but combined with a workable timing theory it can work wonders.

In actual practice it is very hard to force yourself to adopt such contrary frames of mind. Invariably the temptation exists to buy stocks ebulliently just as soon as you sell one at a profit, even though (or perhaps because) the fact is clearly evident that prices have moved strongly upward for some period of time.

The price-motion model and resulting techniques provide excellent objective evidence of market (and individual stock) turning points, but it is indeed difficult to accept and act on the results unless youve trained your emotions to the reverse of the natural bent.

IN A NUTSHELL

chapter eleven

Spectral Analysis - How to Do It and What It Means

• Why Numerical Analysis

• The Meaning of a Frequency Spectrum

• How to Do Fourier Analysis

• Assembling Your Data

• Separating Your Data Into Two Sequences

• Determine the Frequencies in Your Analysis

• Now Compute the Corresponding Amplitudes

• How to Get Composite Amplitudes

• The Kind of Results You Can Expect

• How Numerical Filters Can Help You

• What You Must Know About Filter Operations

• The Part of "Weights" in Numerical Filters

• How to Design Your Own Numerical Filters

• Applying Your Numerical Filter to Stock Prices

• Take Advantage of Curve Fitting

• Fit Your Data Witfi a Straight Line

• How to Use Other Kinds of Curve Fitting

• Summarizing Numerical Analysis

This chapter is provided for those individuals of curious mind who would like to investigate the fascinating intricacies of market cycUcality on their own, but who have little or no background in the required methods of numerical and spectral analysis.

WHY NUMERICAL ANALYSIS

A stock history is a record of a phenomenon; namely, the price changes in a stock as a function of time. Other events of the world also establish such time histories: take the matter of the temperature at a specific location in downtown Los Angeles as an example. This temperature is a quantity which changes continuously as time passes. A pen and ink recorder associated with a suitable thermometer will record a continuous wavy line as temperature changes, minute or large, occur. Such a history is referred to as a continuous "function of time."

A stock price history is a little different. The nature of the events which cause price change is such that the result is not continuous. It is only when a specific transaction takes place that a price change is noted, with the result that stock histories consist of a sequence of price numbers instead of a continuously changing price. Even assuming that stock price changes are a mirror of some unknown continuous variable, such as investor emotional attitudes, does not change the fact that the price changes themselves are only avaHable to us as samples in the form of separate and distinct numbers.

The techniques of numerical analysis were formulated to handle just such problems as ours. What we wish to do is to extract as much information as possible from a time series of discrete numbers. This is precisely what numerical analysis makes it possible to do.

THE MEANING OF A FREQUENCY SPECTRUM

The quantities heretofore referred to as fluctuations, regularities, or periodicities are more precisely called sine waves. A frequency spectrum is a map of the existence and nature of such sine waves. The durations previously referred to are a characteristic of sine waves called the period. The magnitude (or sise) of these is measured from positive peak to negative valley and is known as the amplitude.

In Figure II1-6, two such sine waves are depicted, one of which is slightly displaced from the other in time. This characteristic is spoken of as the phase-relationship of two sine waves. The analogous time relationship of a specific sine wave to an arbitrary (but fixed) reference point in time is similarly noted as the phase time of that particular sine wave.

Thus a sine wave is completely and uniquely described mathematically (or numerically) in terms of the associated period, amplitude, and phase.

Another descriptive quantity can be derived from the period, and is somewhat more useful in numerical analysis. This is the frequency of the sine wave. It is simply computed, once the period is known, by taking the reciprocal of period. In symbols:

It is intended as an introduction to the subject which, when augmented by study of the appropriate references the bibliography, can launch you on your own sea of investigation.