GNPR Distance for Comparing Financial Time Series

Summary

This document describes a Generic Non-Parametric Representation distance for comparing two financial series. It combines a distribution-distance component with a dependence component, with a parameter controlling their relative contribution. The dependence term is based on squared differences between paired observations, while the distribution term uses one-dimensional optimal transport between binned empirical distributions.

The document says the distance is bounded and metric-valued when the parameter is between zero and one. It presents the method as an alternative to a Gaussian approximation and says optimal transport avoids some support-selection issues in histogram-based distance calculations. The bin count can affect computation time. The accompanying code is an implementation reference, not evidence of trading performance; it also cautions that a related parametric approximation may be unsuitable for heavy-tailed data.

Key ideas

• The GNPR distance combines information about marginal distributions and dependence between paired observations.
• A tuning parameter sets the relative weight given to distribution and dependence information.
• The distribution component compares empirical histograms using one-dimensional optimal transport.
• The implementation exposes a bin-count setting that trades computational cost against discretization.
• The document describes a related parametric proxy as less appropriate for heavy-tailed distributions.

Tags

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