Using Fractal Dimension to Distinguish Trends from Cycles

Summary

This document presents a fractal-dimension calculation proposed by John Ehlers and Ric Way as a way to characterize whether price movement is trending or cycling. It starts with median price, applies a short weighted smoothing filter, and compares the price ranges across two halves of a lookback window with the range across the full window. These range measures feed a logarithmic ratio that is smoothed over time to produce the indicator.

The example uses an even-length window, a separate averaging period, and a threshold for interpretation. The text frames the measure as a market-mode sensor, but does not provide empirical results, performance comparisons, or detailed rules for translating readings into trades. Threshold behavior may require calibration to the instrument and timeframe, and the supplied calculation alone does not demonstrate predictive value. The document therefore offers an indicator construction and intended interpretation rather than evidence of a profitable strategy.

Key ideas

• The method uses smoothed median price and compares ranges over two subperiods with the full window.
• A logarithmic ratio of those ranges forms the basis of the fractal-dimension estimate.
• The resulting series is averaged to reduce short-term variation.
• The authors propose using the indicator to distinguish trending from cycling conditions.
• The document gives no empirical test establishing predictive or trading performance.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.