Cycles and
Trading Systems

This time, this Contributing Writer looks at using cycles as the basis of a trading system.

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In previous articles, my search for successful trading systems led me to discover a very effective development methodology: the use of genetic algorithms to find not only appropriate rule parameters, but also optimal combinations of rules chosen from a large set of rule templates I provided. Since then, my intention has been to acquire useful knowledge about the markets that may be cast into rule templates.

With that in mind, I decided to explore some simple but powerful ideas regarding market behavior that could be easily tested in TradeStation. Ideas that prove useful may be cast into rule templates later and incorporated into the genetic search methodology to produce some truly outstanding systems.

In my last article, I began my quest for useful ideas with an exploration of seasonality -- cyclic or recurrent phenomena that are consistently connected in some way to the calendar. I discovered that there are indeed real seasonal effects that would allow an intraday trader to make decisions about tomorrow's trading based on the historical behavior of the market. I also discovered that an end-of-day trader could benefit by using information based on longer-term seasonal trends that indicate the times of the year when the market rises and the times when it declines. Further, I discovered this could be accomplished in a dynamic, adaptive manner. These efforts encouraged me to continue looking for other related market behaviors that could be examined and, if they proved useful, cast into rule templates. This time I'll explore the phenomenon of cycles.
 

WHAT ARE CYCLES?
Basically, a cycle is a rhythmic oscillation. Cycles have frequency (for example, 0.1 cycles per day) or, equivalently, periodicity (for example, 10 days per cycle). Seasonality is a form of cyclic phenomena, one that is induced by the periodicity and recurrence of the seasons, and therefore, one that is tied into an external driving force. However, while all seasonality is cyclic, not all cycles are seasonal. I will attempt to find cycles that are not overtly related to any other kind of phenomenon or driving force, but are merely recurrent rhythms or oscillations in the market.

FIGURE 1: BUTTERWORTH BAND-PASS FILTER. Here's a Butterworth band-pass filter, with a bandwidth factor of 1.25 and center periodicity of 10. Katz has taken a sinewave, swept from a fairly long period to a high frequency (that is, a short period of just a few bars), and passed the sweeping sinewave through the filter. The sinewave appears as the filter input in the bottom graph of Figure 1; this is the driving signal. The top graph shows the output from the filter. At the center frequency, you can see that the output from the filter corresponds closely to the driving signal. They are very much in synchronization; the peak in the driving force is at the peak of the filter, the valleys are also aligned, and the filter output is almost as strong as the driving signal -- there is little or no attenuation.

Figure 1 illustrates the response of a typical Butterworth band-pass filter. I have taken a Butterworth band-pass filter, with a bandwidth factor of 1.25 and center periodicity of 10. I have taken a sinewave, which I've swept from a fairly low frequency (that is, a fairly long period) to a high frequency (that is, a short period of just a few bars), and passed the sweeping sinewave through the filter.

I am going to look for strong signals in the market the way I might look for strong signals using a radio receiver, dialing through the 
different frequencies until I find 
one that comes in clearly.

 
 

The sinewave appears as the filter input in the bottom graph of Figure 1; this is the driving signal. The top graph shows the output from the filter. At the center frequency, you can see that the output from the filter corresponds closely to the driving signal. They are very much in synchronization; the peak in the driving force is at the peak of the filter, the valleys are also aligned, and the filter output is almost as strong as the driving signal -- there is little or no attenuation.

Excerpted from an article originally published in the May 1997 issue of Technical Analysis of STOCKS & COMMODITIES magazine. 
© Copyright 1997, Technical Analysis, Inc. All rights reserved.

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