Polarized Fractal Efficiency
Type
Oscillator
Short introduction
The PFE was introduced in the 1990s by Hans Hannula and is an attempt to transfer ideas from the field of chaos theory and fractal geometry to the study of price movements. The answer of fractal geometry to its classical question: "How long is a coastline?" was: That depends on the resolution with which you view them. What remains constant in many chaotic systems, however, is the degree of fragmentation (the fractal dimension). Applied to price movements, jaggedness can be interpreted as inefficiency of the movement, i.e. low trend strength. The PFE measures this fractal efficiency by looking at price movements at two different resolutions and comparing them with each other. The trend strength is plotted positively or negatively depending on the trend direction (polarized). The indicator therefore oscillates between values of -100% and +100%.
Formula/calculation
Hannula takes a geometric approach to determining the size of price movements, i.e. he does not use the price difference between two points in time, but the length of the (diagonal) connecting line between the points in a line chart. The time axis is measured with the number of periods. The fractal efficiency is the ratio of the length of the (coarse) total line T to the sum of the lengths of the (finer) period movements A, B, C, D (see figure). If all movements in a viewing interval are rectified, a maximum efficiency of 100% is achieved.
Direction = 1, ifCt >Ct-n
Direction = -1, otherwise
Lengtht(m) = SQRT( (Ct -Ct-m)² + m² )
FEt = 100 *Lengtht(n) / (Lengtht(1) + ... +Lengtht-n+1(1))
PFE =EMAz(Direction * FE)
where:
Direction = direction of the trend as the sign of the momentum over n periods
Length(m) = Length of the geometric line between chart points over m periods
FE = Fractal efficiency
n = period number for the trend
z = number of periods for smoothing
Statement/Interpretation
The following literature is recommended for the statement and interpretation of Polarized Fractal Efficiency:
- Hannula, Hans: Polarized Fractal Efficiency, Technical Analysis of Stocks & Commodities, 1/1994
- Florek, Erich: New Trading Dimensions, FinanzBuch Verlag, 2000
- Müller, Thomas and Lindner, Wolfgang: The big book of technical indicators, TM Börsenverlag
Default setting
- n = 10
- z = 5
Basic trading systems
- Polarized Fractal Efficiency (PFE)
In the basic trading system "Polarized Fractal Efficiency (PFE)", the indicator is plotted as an oscillator fluctuating around the zero line together with two auxiliary lines at +40 and -40. The default setting is stored for the parameters: Period 10, GD period 5, price scale 1, price level 100. The "Adaptive" parameter is also activated. The base trading system provides buy signals when the indicator breaks through the line at -40 from bottom to top. These are closed out when the indicator breaks through this line at -40 from top to bottom. It provides sell signals when the PFE breaks through the line at +40 from top to bottom. Similarly, sell signals are closed out when the indicator breaks through this line to the upside.