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The stock market exhibits cyclical trend behavior of sorts, because stock prices tend to move up and down and back again, at various levels. Using Cycle theory, you can exploit the repetitions to predict the next move. So goes the theory! If it's true, you could use it to find the duration of a trend.

In the cyclical approach a number of market forces are said to act on securities independently and concurrently in cyclical fashion and determine prices. To do the computations you assume cycles take the form of sine and cosine functions of trigonometry. (This is Fourier Analysis.) That is, you set each of the concurrent forces equal to an appropriate trig function and add them together to get the overall wave.

As I mention here, viewing the process synthetically -- a process of putting components together -- a number of trig functions can be combined to generate actual price patterns. That is, you start with the parts and come up with the wave.

On the other hand, viewing the actual price pattern itself as a wave, or as the realized sum of component waves, you can analyze it to get the component waves. The analytical procedure is known as spectral analysis and typically invokes Fourier Analysis as a means of identifying the underlying frequency components whose sum makes up the pattern. You start with the wave and find the parts.

As for wave patterns, we can identify three essential properties:

• The period, or the horizontal duration of a complete cycle on the graph.
• The amplitude (or magnitude) -- the vertical distance on a graph from the mid-point to the maximum value of a cycle.
• The phase, or the relative position of one cycle to another -- the horizontal shift of the curve on the graph.

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Referring to Cycles, there are five principles, known as:

• Summation. This principle says the price of stocks is influenced by factors that have varying cyclic properties and can be represented by the (vertical) sum of the components.
• Commonality. This affirms that all securities satisfy the first principle and can be expressed, among other ways, by saying the relative magnitudes of cyclic components are similar in all issues.
• Variation. This states that each cyclic component varies from the ideal due to the fact that magnitude changes slowly as time passes. Magnitude is proportional to duration.
• Nominality. This principle ascribes nominal duration to the main cyclic components.
• Proportionality. This principle says that the duration of a cyclic component relates to the magnitude.

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