The Perfect Cycle
The image below shows a perfect cycle with a length of 100 days. 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). Notice that the cycle crosses the X-axis at 50, 100 and 150, which is every 50 points or half a cycle.
Crest: Cycle high
Trough: Cycle low
Phase: Position of the cycle at a particular point in time (the example cycle is at .95 on day 20)
Inflection Point: This is where the cycle line crosses the X-axis
Amplitude: Height of the cycle from X-axis to peak or trough
Length: Distance between cycle highs or cycle lows
Observe that this is merely a blueprint for the ideal cycle; most cycles are not this well-defined.
Cycle Characteristics
Cycle Length: Lows are usually used to define the length of a cycle and project the cycle into the future. A cycle high can be expected somewhere between the cycle lows.
Translation: Cycles almost never peak at the exact midpoint nor trough at the expected cycle low. Most often, peaks occur before or after the midpoint of the cycle. Right translation is the tendency of prices to peak in the latter part of the cycle during bull markets. Conversely, left translation is the tendency of prices to peak in the front half of the cycle during bear markets. Prices tend to peak later in bull markets and earlier in bear markets.
Harmonics: Larger cycles can be broken down into smaller, and equal, cycles. A 40-week cycle divides into two 20-week cycles. A 20-week cycle divides into two 10-week cycles. Sometimes a larger cycle can divide into three or more parts. The inverse is also true. Small cycles can multiply into larger cycles. A 10-week cycle can be part of a larger 20-week cycle and an even larger 40-week cycle.
Nesting: A cycle low is reinforced when several cycles signal a trough at the same time. The 10-week, 20-week, and 40-week cycles are nesting when they all trough at the same time.
Inversions: Sometimes a cycle high occurs when there should be a cycle low and vice versa. This can happen when a cycle high or low is skipped or is minimal. A cycle low may be short or almost non-existent in a strong uptrend. Similarly, markets can fall fast and skip a cycle high during sharp declines. Inversions are more prominent with shorter cycles and less common with longer cycles. For instance, one could expect more inversions with a 10-week cycle than a 40-week cycle.
Data Categories
The data points on a price chart can be split into three categories: trending, cyclical or random. Trending data points are part of a sustained directional move, usually up or down. Cyclical data points are recurring diversions from the mean. Diversions occur when prices move above or below the mean. Random data points are noise, usually caused by intraday or daily volatility.
Cycles can be found by removing trend and random noise from the price data. Random data points can be removed by smoothing the data with a moving average. The trend can be isolated by de-trending the data. This can be done by focusing on movements above and below a moving average. Alternatively, the Detrended Price Oscillator can be used (see below).
Steps to Find Cycles
freestar
1. Set chart to log scale. (This option can be found under “chart attributes.”)
When looking for cycles, it is important to view price changes in percentage terms instead of absolute terms. On an arithmetic scale, an advance from 100 to 200 will look the same as an advance from 300 to 400. Even though both advances are 100 points, they are much different in percentage terms. A move from 100 to 200 is +100%, while a move from 300 to 400 is +33.3%. On a log scale, the move from 100 to 200 will appear much larger than the move from 300 to 400. This is because the percentage change from 100 to 200 is three times larger. A log scale chart is needed to properly compare price action over a long time period with larger price changes.
2. Smooth the price series with a short simple moving average. This is to eliminate the random noise and focus on the general movements. A short 5-day SMA is often adequate. Smoothing also helps to define reaction lows when volatility is high, such as October-November 2008 in the chart below.
https://www.gold-pattern.com/en
3. Visually analyze the charts for possible cycle lows. This is perhaps the easiest way to find cycles. Find a few lows that appear to have the same cycle length and extend that cycle into the future.
4. Detrend the price series to focus on cycle lows. Detrending can be done with the Detrended Price Oscillator (DPO). This indicator is based on a centered moving average, in other words, a moving average that has been displaced to the left by a factor (N/2 + 1). A 20-day DPO would be based on a 20-day moving average displaced to the left (past) by 11 days [(20/2 + 1) = 11)]. DPO would then be the closing
