Ehlers Loops
Converts price and volume into normalized standard deviation units for scatter plot analysis.
Usage
Use to visualize cycle dynamics in phase-space by plotting the indicator value against its derivative. Loop patterns reveal cycle turns before they appear in the price chart.
Background
Ehlers describes phase-space loops in Cybernetic Analysis as a powerful visualization technique where an indicator is plotted against its first derivative. In cycle mode the path traces elliptical loops; in trend mode the path collapses to a line, enabling visual market mode identification.
Parameters
lp_period(default: 20): Low-pass filter period (SuperSmoother)hp_period(default: 125): High-pass filter period (Butterworth)
Formula
[ HP = c_1 (Price - 2 Price_{t-1} + Price_{t-2}) + c_2 HP_{t-1} + c_3 HP_{t-2} ] [ SS = s_1 \frac{HP + HP_{t-1}}{2} + s_2 SS_{t-1} + s_3 SS_{t-2} ] [ MS = \alpha SS^2 + (1 - \alpha) MS_{t-1} ] [ RMS = \frac{SS}{\sqrt{MS}} ]