# Using Detrending to Help Identify Relevant Cycles

Detrending prices is a common technique used to help identify cyclical market turning points that may otherwise be obfuscated by the trend of the market

Cycle analysts face the challenge of locating major and subordinate cycles that are often shifting, inverting and translating. In addition, a focus on absolute prices and price trends often distracts us from the cyclical aspects of price movement; that is, when prices show trending characteristics, we often overlook the ebb and flow of cycles that occur even within the context of a strong trend.

Falling prey to subjectivity is a criticism often raised in discussions of cycle analysis due to both the nature of cycle studies and the aforementioned seduction of price trends.

Detrending prices is a common technique used to help identify cyclical market turning points that may otherwise be obfuscated by the trend of the market. Detrending also offers some objectivity when searching out important cycles and cycles of different periods. In particular, detrending price using moving averages is the approach often used to provide perspective on market cycles that are hidden inside the broader trend.

This article provides examples of detrending prices using moving averages, offers alternative ways to display them, and applies them to some sample data from the FTSE 100 futures. Experienced readers will note that detrended price creates an oscillator-style indicator that shares some characteristics with other momentum oscillators, including overbought/oversold possibilities and divergence analysis.

**Methods of Detrending**

A detrended price series, resulting in an oscillator-style indicator, is commonly built by comparing price to a moving average. There are several ways to do this, and some are described here. Our experience is that many of the common methods for detrending result in almost identical results; as with much in technical analysis, formulas with greater complexity do not always yield greater trading precision.

The simplest way to conceive of detrending is to imagine a simple moving average plotted horizontally – as the zero line of an oscillator – instead of being displayed as a trendline-like curve on top of the price bars. This has the effect of displaying the prices oscillating around the moving average. The difference between price and the now-horizontal moving average is the oscillator.

The oscillator could simply be the arithmetic difference between the prices and the average, as shown in the middle section of the chart in Figure 1. Although this is likely adequate for most applications, its weaknesses will show over longer time periods and large changes in price.

Also shown in Figure 1 is the difference between price and the moving average as a percent of price instead of a simple difference in points. This has the advantage of keeping the detrended oscillator consistent through different price levels and trends, a primary purpose of this exercise in the first place. This also allows for comparisons across markets, particularly when examining related markets for cycle confluences.

Still another alternative is to use division instead of subtraction in the formula so as to return a ratio; that is, instead of subtracting price from the average, divide the price by the average. Using a ratio has the advantage of returning a “normalized” number similar to the percent calculation mentioned above. The only drawback, and admittedly this is a matter of personal preference, is that the center of this oscillation is 1 instead of 0. This is very minor, but for those accustomed to zero-centered oscillators, this would require a recentering.

Figure 2 displays prices detrended in all three of the ways mentioned. To make the visual comparison easier, a line chart of only the detrended closing prices is shown, unlike the detrended bars displayed in Figure 1. Notice that the third oscillator, labeled “ratio,” is centered at 1. The other two indicators are the close-only versions of those in Figure 1.

Other approaches to detrending prices include offsetting the price and the moving average. An example is to compare the price from a previous bar to the current moving average. The price would generally be from a bar that is half the length of the moving average back from the current price. This has the logical appeal of comparing the price in the center of the time series to the average of the series. There is debate among technicians over whether this would add significantly to the analysis, particularly in light of the delay in making the calculations.

**Identifying Cycles**

Identifying significant highs and lows in absolute price appears easy after the fact. That would make it seem a pretty simple task to lay out useful cycles. Yet the greater challenge is in attempting to identify useful cycles in the midst of a trending market. At these times, the observer can be distracted by the trend and miss important swing points that can be helpful in entries and exits, particularly points to add to or reduce positions within the trend.

In real-world application of this type of analysis, it is important to focus on identifying a recent cycle regime and projecting it forward. This recognizes that although there is persistence in cycles, they also shift as conditions change, requiring ongoing observation and assessment.

In this exercise, we chose to look at 240-minute bars of the FTSE 100 futures. This would generate 5 bars per day, or 25 bars per week. It would also compress the trading hours when the futures are open but the stock exchange is not, so as not to give them undue weight.

The moving average used for detrending has a length of 9 bars. Though this number has no special significance, its selection was not completely random, either. A moving average tends to hide price movements that are within the length of the moving average. That means the length of the average used for detrending and, hence, cycle identification should be less than the length of the cycles one is trying to find. In addition, a whole number factor or multiple of the number of bars per day or week was avoided so as not to be misled into a periodicity that would fall on the same time or day repeatedly.

Figure 3 shows an uptrend period in February 2014, noted by the line AB. The vertical lines mark an 18-bar cycle that was evident following points 1, 2 and 3. Warning signs of a shift in the cycle or the influence of a larger cycle were apparent with the right translation at point a and the inversion of the cycle at point b.

This prompted us to note the possibility of a 54-bar cycle as noted by the arcs. Further evidence of this came at point 4. Both these cycles are, of course, perfect multiples of 9 and one should not expect to find such neatly nested cycles.

Did these observations prove useful as later price action unfolded? Here, we scroll ahead to the period in late March (line CD) and the uptrend period from mid-April to mid-May (line EF). (Readers are invited to examine the period between Figures 3 and 4; it shows some interesting action in the context of these cycles.)

The broader 54-bar cycle identified the bottoming period at CD, with the confluence of the two cycles coming along with the volatility of the basing between points 5 and 6, with point 6 being within just a few bars of the start of the uptrend. Point 7 is notable for the cycles again bottoming together and the uptrend showing healthy acceleration from that point. Readers are also encouraged to look at the 108-bar cycle, as measured forward from the February period.

**Conclusion**

Identifying cycles can be a challenge in the best of circumstances. This is especially so in trending markets when the force of absolute price masks the cyclical action beneath. Detrending of prices is a useful method that aids in exposing cyclical price movement, particularly during such strongly trending periods. Combine a moving average of a length within the general cycle framework with even the simplest detrending method, and you may find a different perspective on the ebb and flow of prices.