**Cycles:**

A cycle is an event, such as a price high or low, which repeats itself on a regular basis. Cycles exist in the economy, nature and the financial markets. The basic business cycle encompasses an economic downturn, bottom, economic upturn and top. Cycles in nature include the four seasons and solar activity (11 years). Cycles are also part of technical analysis of the financial markets. Cycle theory asserts that cyclical forces, both long and short, drive price movements in the financial markets.

Price and time cycles are used to anticipate turning points. Lows are normally used to define cycle length and then project future cycle lows. Even though there is evidence that cycles do indeed exist, cycles change over time and even disappear at times. While this may sound discouraging, trend is the same way. There is indeed evidence that markets trend. but not all the time. Trend disappears when markets move into a trading range and reverses when prices change direction. Cycles can also disappear and even invert. Do not expect cycle analysis to pinpoint reaction highs or lows. Instead, cycle analysis should be used in conjunction with other aspects of technical analysis to anticipate turning points.

**The Perfect Cycle**

The image below shows a perfect cycle with a length of 100 days. Not all cycles are this well-defined. This is just a blueprint for the ideal cycle. The first peak is at 25 days and the second peak is at 125 days (125 - 25 = 100). The first cycle low is at 75 days and the second cycle low is at 175 days, also 100 days later. Also notice that the cycle crosses the Y axis at 50, 100 and 150, which is every 50 points or half a cycle.

*Crest: Cycle high

*Trough: Cycle low

*Phase: Position of cycle on particular point in time. This cycle is at .95 on day 20.

*Inflection Point: This is where the cycle line crosses the Y axis.

*Amplitude: Height of the cycle from Y axis to peak or trough.

*Length: Distance between cycle highs or cycle lows.

**Predicting Stock Market Using Cycle Analysis and Synthesis:**

Investors could benefit from a fluctuating nature of the stock market. A semi-cyclical nature of the market is a bad surprise for some investors but others know how to take advantage of the cycles. To discover cyclical patterns in the market movement, investors use different software tools.

Stock market cycles may help to maximize ROI.

One of the stock market characters is that it has powerful and pretty consistent cycles. Its performance curve can be considered as a sum of the cyclical functions with different periods and amplitudes. Some cycles known by investors for long, for example, four-year presidential cycle or annual and quarterly fiscal reporting cycles. By identifying the cycles it is possible to anticipate tops and bottoms, as well as, to determine trends. So that the stock market cycles can be a good opportunity to maximize return on investments.

**It is hard to identify cycles using a simple chart analysis.**

It is not easy to analyze the repetition of typical patterns in stock market performance because often cycles mask themselves; sometimes they overlap to form an abnormal extreme or offset to form a flat period. The presence of multiple cycles of different periods and magnitudes in conjunction with linear and non-linear trends can form a complex pattern of the curve. Evidently, a simple chart analysis has a certain limit in identifying cycles parameters and using them for predicting. Therefore, a mathematical statistical model implemented in a computer program could be a solution.

Be aware: no predictive model guarantees 100% precision.

Be aware: no predictive model guarantees 100% precision.

Unfortunately, any predictive model has own limit. The major obstacle in using cycle analysis for the stock market prediction is a cycle instability. Due to a probabilistic nature of the stock market cycles, the cycles sometimes repeat, sometimes not. In order to avoid excessive confidence and, therefore, losses it is important to remember about a semi-cyclical nature of the stock market. In other words, the prediction based on cycle analysis, as well as, any other technique cannot guarantee 100% accuracy of prediction.

**Back-testing helps to improve prediction accuracy.**

One of the techniques to improve a prediction accuracy is back-testing. It is the process of testing prediction on prior time periods. At the beginning, instead of calculating the prediction for the time period forward, we could simulate the forecast on relevant past data in order to estimate the accuracy of prediction with certain parameters. Then the optimization of these parameters could help to reach a better precision in forecast.