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A spectrum display shows amplitude on the Y axis vs. cycle length on the X axis. This display allows you to see the relative strength of several cycles, a benefit beyond merely picking out the dominant cycle. The spectrum display also allows you to identify the quality, or resolution of the cycle measurement.

Ideally, a cycle measurement is a single spike on the display. This ideal picture tells you that there is only one well-defined spectrum component — the dominant cycle. But what if the spectrum display is a broad bell-shaped curve? In this case, the energy is spread over a range of possible dominant cycles, with no cycle length being clearly dominant. The spectrum display indicates that the lack of resolution is reason enough not to trade the market on the basis of cycles. For trend identification we are most interested in the capability of the spectrum display to show the formation of two or more cycles.

Figures 4, 5 and 6 show the progression of the spectrum for the next three trading days. Figure 6 is the spectrum for 900302, the day we previously declared the trend to be established.

J.M. Hurst, in The Profit Magic of Stock Transaction Timing, advances the principle of proportionality. Simplified, the principle states that longer cycles have larger amplitudes. This principle is obvious to the most casual chart reader.

We can use this principle to identify trends with the spectrum display of short-term cycles. From our example for gold, Figure 2 shows an excellent 12-day cycle on 900222, just after we entered our short position. Figure 3 shows the spectrum taken on 900227. The very long cycle, longer than 50 days, is starting to appear. Figures 4,5 and 6 show the progression of the spectrum for the next three trading days. Figure 6 is the spectrum for 900302, the day we previously declared the trend to be established. Figure 7 shows the spectrum three trading days later on 900307. Figure 7 shows that the short-term cycle has been

swamped by the trend, which is interpreted as a long cycle outside the calculation range. Used this way, the spectrum confirms that the trend has been established.

The spectrum can also confirm that the trend movement has ended. The price first crosses the instantaneous trendline from the bottom on 900418. (We could have exited then at about 385 for a total profit of $4,600 on a single contract.) Figure 8 is the spectrum for 900418, and shows long cycle energy. Figure 9 is the spectrum for 900425, five trading days later. Absence of long cycle energy confirms the trend has ended.

I'm trying to automate the entire trading strategy. One of the early dreams for computers, you may recall, was to create robots to serve mankind.

Helpful cycles and trading strategy

Our example is not an uncommon event. This approach can be used to repeatedly alter your trading strategy as the market shifts from the cycle mode to the trend mode. All you need to do is estimate or measure the current short-term cycle and then take a simple average over the period of the cycle length and plot it as a point on your bar chart. Repeat this daily. Connecting the averages with a line creates your "instantaneous trendline." Then watch the price action relative to this trendline to identify the onset of the trend when the price has not crossed within the last half cycle.

I'm trying to automate the entire trading strategy. One of the early dreams for computers, you may recall, was to create robots to serve mankind. By recognizing when we are in a trend mode (Diffusion Equation) or cycle mode (Telegrapher's Equation), our computers should know when to apply the proper trading strategy. I guess that would make our computer a "know-bot"!