Interpolated ECDFs and Rank-Based Pair Selection for Copula Trading

Summary

This reference explains two utilities for copula-based trading research: a linearly interpolated empirical cumulative distribution function (ECDF), and a quick selector for candidate pairs. A standard empirical CDF is a step function, which can map sparse observations to repeated quantiles and can return boundary values of zero or one. The described interpolation is designed to smooth those mappings and keep values inside the range needed by some copula calculations. An example applies a mapping trained on one portion of price data to a later portion.

For pair selection, the methods are Kendall's tau, Spearman's rho, and Euclidean distance on normalized prices. The text describes the rank correlations as nonparametric, notes Kendall's greater stability and lower sensitivity to outliers, and reports that Euclidean-distance rankings often disagree with rank-based rankings and performed less suitably in the authors' backtests. Illustrations use Dow stock data from 2011–2019. These observations are descriptive rather than proof of future profitability; pair rankings depend on the sample and should be evaluated out of sample.

Key ideas

• A conventional ECDF is a step function and may produce boundary quantiles that complicate copula calculations.
• Linear interpolation is used to smooth quantile mapping and avoid exact zero and one outputs.
• Kendall's tau and Spearman's rho offer rank-based ways to rank candidate pairs.
• The authors describe Kendall's tau as more stable and less affected by outliers than Spearman's rho.
• Euclidean distance can identify different pairs, and the document reports weaker suitability for copula strategies in its backtests.

Tags

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