The Hiemstra-Jones Test Revisited

TL;DR

This paper critically revisits the Hiemstra-Jones test for nonlinear causality, identifying inconsistencies in its estimators and proposing new estimators with reestablished asymptotic properties to improve test accuracy.

Contribution

It introduces corrected estimators for the HJ test's probabilities and reestablishes their asymptotic properties, addressing over-rejection issues in previous applications.

Findings

New estimators are consistent with the original criteria.

Reestablished asymptotic properties support the validity of the new test.

Simulations demonstrate improved performance over the original HJ test.

Abstract

The famous Hiemstra-Jones (HJ) test developed by Hiemstra and Jones (1994) plays a significant role in studying nonlinear causality. Over the last two decades, there have been numerous applications and theoretical extensions based on this pioneering work. However, several works note that counterintuitive results are obtained from the HJ test, and some researchers find that the HJ test is seriously over-rejecting in simulation studies. In this paper, we reinvestigate HJ's creative 1994 work and find that their proposed estimators of the probabilities over different time intervals were not consistent with the target ones proposed in their criterion. To test HJ's novel hypothesis on Granger causality, we propose new estimators of the probabilities defined in their paper and reestablish the asymptotic properties to induce new tests similar to those of HJ. Some simulations will also be presented to support our findings.