A Mutual Information Approach to Calculating Nonlinearity

TL;DR

This paper introduces a mutual information-based method to quantify nonlinear dependence between variables, distinguishing linear and nonlinear components, and compares it with the BDS test for linearity.

Contribution

It presents a novel mutual information approach for measuring nonlinearity and provides an exact calculation of linear dependence proportion, enhancing analysis of variable relationships.

Findings

The method accurately quantifies nonlinear dependence.

It provides an exact measure of linear dependence proportion.

Comparison shows advantages over the BDS test.

Abstract

A new method to measure nonlinear dependence between two variables is described using mutual information to analyze the separate linear and nonlinear components of dependence. This technique, which gives an exact value for the proportion of linear dependence, is then compared with another common test for linearity, the Brock, Dechert and Scheinkman (BDS) test.