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A Consistent Nonparametric Test for Granger Non-Causality Based on the Transfer Entropy.

Cees Diks1,2,3, Hao Fang1,4

  • 1Center for Nonlinear Dynamics in Economics and Finance (CeNDEF), University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

We developed a new statistical test for Granger non-causality using a Taylor expansion of transfer entropy. This method overcomes previous limitations, enabling robust analysis of causal relationships in financial data.

Keywords:
Granger causalityU-statisticfinancial time serieshigh frequency datanonparametric test

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Area of Science:

  • Econometrics
  • Time Series Analysis
  • Nonparametric Statistics

Background:

  • Transfer entropy is a powerful measure for assessing Granger non-causality.
  • Kernel density-based nonparametric estimators of transfer entropy face challenges due to intractable asymptotic distributions.
  • Existing methods for Granger non-causality testing are limited by these estimation difficulties.

Purpose of the Study:

  • To develop a novel, tractable statistical test for Granger non-causality.
  • To overcome the limitations posed by the asymptotic distribution of transfer entropy estimators.
  • To provide a reliable method for analyzing causal relationships in time series data.

Main Methods:

  • Utilized a first-order Taylor expansion of transfer entropy near the null hypothesis of no Granger causality.
  • Expressed the estimated Taylor expansion as a U-statistic to ensure asymptotic normality.
  • Conducted numerical simulations to evaluate the size and power properties of the proposed test.

Main Results:

  • The proposed test, based on the Taylor expansion, demonstrates asymptotic normality.
  • Numerical studies confirm the favorable size and power characteristics of the new test.
  • Empirical applications to stock indices and exchange rates showcase its practical utility.

Conclusions:

  • The developed Taylor expansion-based test offers a statistically sound and computationally tractable approach to Granger non-causality.
  • This method effectively addresses the limitations of previous transfer entropy-based tests.
  • The test is applicable to real-world financial time series, facilitating improved causal inference.