Testing Correlation Cones with Monomorphic Pull-Backs and Push-Outs

Summary

The article explores category-theory constructions as a way to organize correlations between currency pairs and a dollar index. It first sketches coequalizers as a possible way to combine trading-session drawdown observations into a conservative value for position sizing. Its main example builds cones from correlations over Fibonacci-like lookback periods, combining EURUSD and USDJPY correlations with a transformed geometric mean and comparing the result with EURJPY observations.

The author reports weekly tester logs over roughly six months and finds that selecting the period with the highest USDX correlation does not accurately project EURJPY correlation. Restricting the cone through monomorphic pull-backs and epimorphic push-outs changes reported outcomes by sizable percentages. The evidence is exploratory and limited to the stated instruments, timeframe, and sample; the article does not establish predictive validity or trading profitability. Its category-theory framing is an experimental data-organization approach rather than a validated forecasting method.

Key ideas

• The article represents currency-pair correlation series and lookback periods as domains connected in a cone.
• It combines EURUSD and USDJPY correlations using a geometric mean after shifting values to handle negative correlations.
• The reported test finds that selecting the strongest USDX correlation period does not accurately project EURJPY correlations.
• Changing cone composition with monomorphic or epimorphic constraints can materially alter the reported outputs.
• The short exploratory sample does not demonstrate a reliable trading signal or profitable strategy.

Tags

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