TASC 2022.06 Ehlers Loops

May 13, 2022

█ OVERVIEW


TASC's June 2022 edition Traders' Tips includes an article by John ​Ehlers titled "Ehlers Loops. Part 1". This is the code implementing the price-volume Ehlers Loops he introduced in the publication.



█ CONCEPTS


John ​Ehlers developed Ehlers loops as a tool to visualize the performance of one data stream versus another, both filtered and scaled. In this article, the author applies his concept to exploit and/or dispel the dogmatic principles of reliable price-volume relationships.

The script offers two different ways to visualize ​Ehlers Loops:


Oscillators (default option)

In this implementation, filtered and scaled ​volume is plotted along with filtered and scaled price as zero-mean oscillators. Observation of the relative direction of ​volume and price oscillators can be discretionarily used to interpret and predict market conditions. For example, it is generally assumed that an increase in ​volume and an increase in price define a ​bullish condition. Similarly, decreasing ​volume and increasing price are generally considered ​bearish. A decrease in ​volume and a decrease in price is considered a ​bullish condition. The increase in ​volume and decrease in price is often thought to be ​​bearish.


Scatterplot

This Crocker-style visualization displays filtered and scaled price against filtered and scaled ​volume for the selected timespan. Fluctuations in ​volume are plotted along the x-axis, while price changes along the y-axis. This way of visualizing the ​Ehlers Loop allows you to analyze the curvature and directional path of the price in relation to ​volume, offering a different comparative perspective. The boundaries of the price and ​volume scale on the ​Ehlers Loop Crocker-chart are presented in standard deviations. Deviations can be used to predict possible future price or ​volume fluctuations. The expected probability of potential reversals is 68%, 95% and 99.7% at one, two and three standard deviations, respectively.



█ CALCULATIONS


The following steps are used to build an ​Ehlers Loop:
 • Both price and ​volume are filtered to be band-limited signals. This is done by applying the high-pass Butterworth filter in combination with the low-pass SuperSmooth filter.
  The cutoff wavelengths of the high-pass and low-pass filters are defined by the input parameters HPPeriod and LPPeriod, respectively.
  These values change the appearance of the ​Ehlers Loops and can be customized to your trading style.
 • The filtered price and ​volume time series are then scaled in terms of standard deviation by dividing each by their root-mean-square values.
 • The resultant price and ​volume data are plotted as zero-mean oscillators or as a scatterplot.