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Cycle analysis can help you choose a stock depending on your preferred holding period

Cycle analysis is one of the most difficult aspects of technical analysis. It is the basis of complex tools such as Elliot Wave theory and Fibonacci Analysis. A basic understanding of cycles can aid the practical trader.

Most traders base holding period on considerations such as their bank account, the required margin. For example, a day trader will study data in 5-minute or 30- minute ticks and apply Moving Averages or Rate of Change and other indicators at multiples of these periods.

Another trader will use 3 or 5 day averages, while a long-term player will apply 30 day or 200 daytimeframes.But different stocks move in different cycles and the trader may pick a stock that isn't optimally traded at his favourite timeframe. This is where cycle analysis is useful.

Let's first define a cycle. A full cycle is the period from one peak to the next peak or from one trough to the next trough. A rule of thumb for choosing indicators is the timeframe is approximately half that of the full cycle. That is, if the stock goes from one peak to the next peak in say, 100 periods, then the optimal indicator timeframe will be 50 periods.

In practice, analysis in different timeframes will reveal different sets cycles. We need to set our basic time period unit. This can be anything - scale up to a weekly unit, or down to 5-minutes as required. Ignore holidays when calculating time periods - cycle calculation is by the number of trading periods. This means adjustments for 4-day weeks and circuit breakers.

Please use your judgment. Some calculate "artificial weeks" of any 5-day successive periods, and others calculate artificial days of 30-minute ticks ignoring circuit breakers. This method can "underweight" closing prices, which many traders consider highly significant.

Stocks rarely perform successive cycles in exactly the same periods. The trader will have to adjust by taking an average. This may not be an arithmetical average, it could also be a median or a modal value of the cycle distribution.

The calculation is tedious but not difficult. Some TA packages include spectrum analysis tools, which allow more systematic calculation. The mathematics is beyond our current scope but engineering students will note that these adapt Fourier Transforms from similar problems in digital filter designs.

Here's a typical example of cycle analysis, which illustrates the problem and advantages. Assume that the trader is interested in picking up the dominant cycle of the daily Sensex. Take the HLOC daily bar-chart of Sensex for the last 100 periods.

The chart has been displayed with the successive Peaks and Troughs labelled "P" and "T" respectively. It may be noted that the succeeding cycles are often of unequal lengths. The trader can deal with this in several ways.

One useful method is to set a cut-off "significance value". Eliminate all peaks/troughs that are not say, 1 per cent higher/lower than the preceding and succeeding bars respectively. Another method is to eliminate successive troughs/ peaks that occur without an intervening move in the opposite direction.

This isolates "true" peaks and troughs.We have not eliminated here in the chart to show the practical problem. But we have eliminated in calculations by using the second method (no successive troughs/ peaks without intervening opposite moves)in making the calculations.

The trader can calculate the days between successive peaks and troughs to extract the length of each cycle. By our methods, after elimination, there have been seven troughs, and six peaks. The longest trough -trough (T-T) period is 20 periods while the longest peak -peak (P-P) period is 21. The shortest T-T is 5 while the shortest P-P is 4.

The mean T-T is 12.71 while the mean P-P is 12.67 - close enough. We can reasonably assume that a completeSensex cycle usually occurs every 12-13 days. The median T-T value is 11 while the median P-P value is 14. How does this help? The trader can set timeframes at around 6-7 days for indicators using the "half-the-cycle" rule.

He can also start looking forthe next trough or peak by marking off the chart for every 12-13 sessions. If this cycle timing doesn't suit his personal favourite holding period, he should not play the stock concerned.