Optimal Copula Transport for Measuring Dependence
Summary
The document describes an optimal transport measure that compares the empirical dependence between two data series with a chosen target copula. It first converts paired observations to ranked uniform values, then measures transport distances from that empirical copula to both the target and an independence reference. The dependence score is defined from those distances, so it indicates how much the observed structure resembles the selected target relative to independence.
The implementation supports targets including comonotonic, countermonotonic, Gaussian, mixed-sign, variation-dependent, and V-shaped dependence. Gaussian and some other targets are generated with random samples, as is the independence reference, so repeated runs may produce different values unless randomness is controlled. The document gives code and parameter descriptions but no empirical tests, calibration guidance, or trading results. The score also depends on the target selected and should be treated as a dependence diagnostic, not evidence of predictive or profitable trading behavior.
Key ideas
- Rank-transform paired observations to represent their empirical copula.
- Compare the empirical copula with a selected dependence target and an independence reference using optimal transport distances.
- Interpret the score relative to the chosen target, since different target copulas describe different dependence patterns.
- Randomly generated target and reference samples can make results vary across runs.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.