Using Category Theory Equalizers to Compare ATR Forecasts

Summary

The article introduces category theory equalizers as a way to identify input cases where two mappings agree, then applies the idea to forecasting changes in bar range from changes in ATR. It normalizes both series as percentage changes, groups them into bands, and defines one mapping as a theoretical hypothesis that ATR and range changes move in the same direction. A second mapping comes from a training sample that counts the observed range-change band after each ATR-change band.

The proposed equalizer consists of ATR-change cases where the hypothesis and empirical mapping agree; the author suggests using those cases for out-of-sample forecasts and skipping other cases. The illustration refers to a EURGBP five-minute sample over a stated date range, and displayed mapping examples use EURUSD. The article provides no performance metrics or validation results. Its relation analogies and mapping terminology are informal, and it cautions that more complex fits can overfit, recommending longer tests and broker real-tick data.

Key ideas

• An equalizer identifies inputs on which two mappings from the same domain produce matching outputs.
• The example compares a theoretical ATR-to-range mapping with a mapping estimated from historical band counts.
• Percentage changes are grouped into discrete bands to make ATR changes and later bar-range changes easier to compare.
• The proposed forecast uses only ATR-change cases where the two mappings agree and otherwise waits.
• The article gives no measured forecasting performance and warns against overfitting more complex mappings.

Tags

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