A multivariate distance nonlinear causality test based on partial distance correlation: a machine learning application to energy futures

Abstract

This paper proposes a multivariate distance nonlinear causality test (MDNC) using the partial distance correlation in a time series framework. Partial distance correlation as an extension of the Brownian distance correlation calculates the distance correlation between random vectors X and Y controlling for a random vector Z. Our test can detect nonlinear lagged relationships between time series, and when integrated with machine learning methods it can improve the forecasting power. We apply our method as a feature selection procedure and combine it with the support vector machine and random forests algorithms to study the forecast of the main energy financial time series (oil, coal, and natural gas futures). It shows substantial improvement in forecasting the fuel energy time series in comparison to the classical Granger causality method in time series.

Keywords:

• Financial forecasting
• Lead-lag relationship
• Nonlinear correlation
• Energy finance
• Support vector machine
• Brownian partial distance correlation
• Random forests

Acknowledgments

The authors thank Maria Rizzo, Hamed Ghoddusi, Dror Kennett, Alex Moreno, Gary Kazantsev, two anonymous referees, and the participants of the Eastern Economics Association meeting 2014, and the 11th International Conference on Computational and Financial Econometrics 2017, for their comments and suggestions; and to Patrick Jardine for proofreading this paper. The opinions presented are the exclusive responsibility of the author.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Germán G. Creamer http://orcid.org/0000-0002-3159-5153

Chihoon Lee http://orcid.org/0000-0001-5448-2787

Notes

1 Information about R can be found at <http://cran.r-project.org>.