Using a Category Theory Naturality Square to Forecast Volatility
Summary
The article explains natural transformations through two functors that map normalized changes in ATR and Bollinger Bands to price-range changes. Indicator changes are discretized into 21 bins from −100% to 100%, while price-range changes are stored as unrounded fractions. The four resulting codomain objects represent one-bar and two-bar range changes for the two indicators.
The proposed forecasting focus is the naturality square: relationships among those four price-range objects are used to project volatility changes. The article illustrates the commuting-square idea with a separate example of lists and lists of lists, and discusses mappings that could be learned with methods such as multilayer perceptrons. It also mentions possible extensions to entry and exit signals or position sizing. No forward-run results validate the approach; the author explicitly says the supplied settings may need modification or combination with other strategies. The indicator-to-range functors provide conceptual context, while the claimed forecast relies primarily on the codomain structure.
Key ideas
- A natural transformation connects two functors through morphisms between their outputs while preserving relationships in the source category.
- ATR and Bollinger Bands changes are normalized and assigned to 21 discrete values spanning −100% to 100%.
- Four price-range objects encode changes across different one-bar and two-bar horizons.
- The proposed volatility forecast uses relationships among the four codomain objects in a commuting naturality square.
- The article supplies no forward testing evidence and cautions that its settings may require changes.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.