The Polarized Fractal Efficiency indicator by Hans Hannula shows how efficient, meaning how much like a straight line, the price movement has been over the past N days.
The net distance travelled over the past N days is expressed as a percentage of the total of each day’s distance travelled. Distance is measured in two-dimensions, like a ruler on the plotted graph. Rise (or fall) is expressed as a percentage, and each day counts as 1 unit across. So the formula, on closing prices p1 (today) to pN is
Sign(p1-pN) * Hypot(N-1, Pchg(p1,pN)) PFE = 100 * ------------------------------------------------------- Hypot(1, Pchg(p1,p2)) + ... + Hypot(1, Pchg(p[N-1],pN)) Sign(X) = 1 if X>0, or -1 if X<0 new - old Pchg(new,old) = 100 * --------- old Hypot(x,y) = sqrt (x^2 + y^2)
Here “Pchg” is a percentage change up or down from “new” to “old” price, and “Hypot” is the distance (the hypotenuse) for a move of X horizontally and Y vertically. “Sign” means that PFE is positive or negative according to whether the change over the past N days is up or down.
At the extremes of 100 or -100, price movement is at maximum efficiency, with the past N days making a perfectly straight line. An almost straight line is generally very close to 100 too. A midpoint of 0 means there’s been no net change over the past N days.
Hannula looked at price changes over 10 day period (horizontal distance of 9), and this is the default in Chart. A smoothing parameter is provided too; it applies an exponential moving average (see Exponential Moving Average) to the PFE. The default is 5 days smoothing, a value of 0 means no smoothing (to see the raw values).
Copyright 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2014, 2015, 2016, 2017 Kevin Ryde
Chart is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.