Introduction
The origin of the theory of business cycles can be traced back to the 18th century, when economists such as Juglar, Kitchin and Kondratief became famous for finding specific cycles in business activities. The big breakthrough in modern cycle analysis came when ER Dewey set up the Foundation for the Study of Cycles in Pittsburgh in 1940. Thereafter the statistical evidence that cycles exist in many economic series was proved conclusively.

Cycle Theory
Practical cycle theory assumes that cycles that consistently persist in data and are repetitive will continue to do this in the future. Cycles that have performed well in the past should continue this into the future, if they are genuine. These cycles can be used for forecasting. Up to now the two most used cycle techniques were Spectral Analysis and Maximum Entropy Spectral Analysis (Mesa).

Cycle Trends Method
The Cycle Trends method starts with a stationary series i.e. a de-trended series. To de-trend the series a proprietary Fourier filter is used. (The blue line on the price graph). There are many advantages to the Fourier filter, such as, that it does not lose end points as a centered moving average filter would do.

The Fourier filter is basically a regression method, meaning that history changes as you move on in time, deleting old data and adding new data.

There are two cycle indicators in the Cycle Trends program.

1. The Cycles-Trig indicator. Cycles of a specific shape viz. a sinusoidal shape filtered via trigonometric regression.

2. The Cycles-Array indicator. Cycles may be of any shape from square to triangular to sinusoidal.

The program is designed to find those cycles, from past data, that are repetitive, do this consistently and do not fade away. Because they are repetitive they can become predictable and be used for forecasting.

Cycles are described as sine waves and have frequency, amplitude and period. The amplitude is important, as it is proportional to the strength of the cycle. Knowing the period of the cycle allows analysts to use short periods for trading and longer periods for investing or to gauge the longer-term trend. Cycle Trends works on 900 days and optimally looks for cycles that repeat themselves ten times or more.

The analyst requires the following information from the cycles.

· When did, or when will the major peaks or lows occur?
· Are they near in terms of time or have they just past?
· What is the short and long term trend of the financial instrument under analysis?

The cycles in the program are developed in two stages.

Stage 1
The program examines each cycle and then isolates those that are repetitive and have the largest amplitudes. The fit of each cycle to past data is also computed and this is also included in the selection process. From the foregoing, 20 cycles (on average) are selected from the data series for examination.

Stage 2
In the second phase the statistic reliability of each cycle is tested. The object here is to exclude cycles that have been influenced by random events e.g. wars, sudden catastrophes, etc.

The Bartels Test is used for this. The Test was developed by Julius Bartels, a geophysicist who worked at the Carnegie Foundation in Washington in the 1930's. There is detailed mathematics behind the Test, which measures the stability of the amplitude and phase of each cycle.

The method provides a direct measure of the likelihood that a given cycle is genuine. The closer the cycle statistic is to 100%, the less likelihood it is that the cycle is not genuine and has been influenced by random events.

From the above, the program allows the analyst to examine a Cyclegram of the financial instrument he is examining. He will develop graphs from this Cyclegram. This applies to indexes, individual stocks, currencies, bonds, commodities etc.

An example is shown here of the Cyclegram of the Dow Jones Industrial Average based on the closing price of 7568 on March 10, 2003.

Cyclegram
The Cyclegram is divided into 5 columns.

Number:
The number of the cycle. There are on average approximately 20 cycles in the daily and 10 in the weekly cycle input.

Period:
The period (length) of the cycle in days, weeks, bars etc.

Amplitude:
The cycle amplitude strength. This is the vertical distance from the minimum to the maximum of a cycle. Long period cycles usually have proportionally larger amplitudes. Cycles with larger amplitudes are significant, especially if they occur in those with short periods.

Fit (%):
Percentage fit is a statistical measure of the historic fit of the cycles to the de-trended data. Cycles can be selected for the forecast according to their percentage fit. The statistics tell you how well a cycle had fitted the price movements in the past and is likely to do the same in the future.

Bartels:
This statistic is a percentage measure of the likelihood that a given cycle is genuine. The closer the cycle statistic is to 100%, the less likelihood it is that the cycle has been influenced by random events.

Note that three of the cycle periods in this Dow Jones example have Bartel percentages above 90%. This points to a successful forecast.

Finding the Right Cycle
The success of a cycles forecast is dependent on the choice of the right cycles by the analyst. Finding the right cycles can be compared to tuning into the radio and turning the dial until the desired station comes in, and avoiding the static (noise) in between.

High frequency, shorter cycles are more easily identified than the longer, low frequency cycles. The strength or amplitude of a cycle is generally proportional to its length. A long cycle is usually very strong, a shorter cycle comparatively weak. Although shorter cycles individually do not have much strength, collectively their amplitudes could add up to significant price movements and their combined influence can move the market quickly up or down.

Shorter period cycles therefore, when combined, can provide reasonably accurate forecasts of what the market is likely to do in the future.

Cycles indicate what the market is likely to do, but does not guarantee what it will do. Skills are needed by the analyst to use the correct cycles. His judgement should be backed and confirmed by other indicators and fundamentals.

Cycle Combinations
As stock market cycles are irregular it is necessary to use cycle combinations to narrow down the forecast to a sufficiently small time span. The analyst can combine the cycles in different combinations, depending on whether he is looking for short or long-term forecasts. These are then projected into the future zone, for the forecast. He would use the longer-term period cycles for long term forecasts and the shorter period cycles for trading. Single short period cycles, with high Bartel percentages can be used for trading as well.

Example
As an example, using the Bartel trading cycles, a short-term forecast is made for the Dow Jones Industrial Index, on March 10, 2003, based on the cycles generated by the program, as seen in the previous Cyclegram.

The cycle low is seen at Point A, corresponding to the price of 7568 (also Point A).

The cycle forecasts a steep rise in March, topping out towards the month's end (note the monthly demarcations).

Note that the Dow reached 8521 on March 21.

Deciding if the Cycle Combination is Correct
Cycle programs are designed to give analysts the opportunity to show cycle lows and peaks and thus provide low risk opportunities. Not all cycles will give the correct information. Deciding if the cycle combination is correct can be made by making certain that the cycle combination fits the price movement of the immediate past  if not, other cycle combinations can be used.

Cycle patterns in the future zone are significant as well. A sharp pattern in a straight line, that trends up or down from a sharp point gives excellent results, as can be seen in the example shown of the Dow Jones on March 10.

Confirming Cycle Readings
Cycles should not be relied on their own when making investment decisions. They should be backed up by other standard technical indicators as well. Overbought/Oversold and Stochastic indicators are very useful in this regard.