A permutation entropy based test for causality: The volume–stock price relation

• A novel statistic for detecting causality in nonlinear processes is presented.
• The statistic captures causality in conditional mean and in conditional variance.
• The new test is compared with other well-established tests.
• The causal relation between trade volume and stock prices is studied.

The purpose of this paper is to propose a newly developed non-parametric test for linear and nonlinear causality based on permutation entropy and to show its usefulness in analyzing the potential causal relationship between trading volume and security prices. Most of the empirical applications and tests for causality rely on using Granger causality based test for linear models. Although these tests have high power in uncovering linear causal relations, their power against nonlinear causal relations can be low. Our test is designed to deal with the detection of linear and non-linear causality. We also compare our permutation entropy based test with other Granger causality tests. Monte Carlo simulations show excellent performance (in terms of size and power) of the new test for detecting linear and non-linear causality under different scenarios. Our conclusions point that there is a bidirectional causal relation from volume to price returns not only in the mean but also in the variance.