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Entropy 2014, 16(4), 2309-2349; doi:10.3390/e16042309

Measures of Causality in Complex Datasets with Application to Financial Data

1
Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
2
Systemic Risk Centre, London School of Economics and Political Sciences, London WC2A2AE, UK
*
Author to whom correspondence should be addressed.
Received: 8 January 2014 / Revised: 10 March 2014 / Accepted: 8 April 2014 / Published: 24 April 2014
(This article belongs to the Collection Advances in Applied Statistical Mechanics)

Abstract

This article investigates the causality structure of financial time series. We concentrate on three main approaches to measuring causality: linear Granger causality, kernel generalisations of Granger causality (based on ridge regression and the Hilbert–Schmidt norm of the cross-covariance operator) and transfer entropy, examining each method and comparing their theoretical properties, with special attention given to the ability to capture nonlinear causality. We also present the theoretical benefits of applying non-symmetrical measures rather than symmetrical measures of dependence. We apply the measures to a range of simulated and real data. The simulated data sets were generated with linear and several types of nonlinear dependence, using bivariate, as well as multivariate settings. An application to real-world financial data highlights the practical difficulties, as well as the potential of the methods. We use two real data sets: (1) U.S. inflation and one-month Libor; (2) S&P data and exchange rates for the following currencies: AUDJPY, CADJPY, NZDJPY, AUDCHF, CADCHF, NZDCHF. Overall, we reach the conclusion that no single method can be recognised as the best in all circumstances, and each of the methods has its domain of best applicability. We also highlight areas for improvement and future research. View Full-Text
Keywords: causality; Granger causality; Geweke’s measure of causality, transfer entropy; ridge regression; cross-covariance operator causality; Granger causality; Geweke’s measure of causality, transfer entropy; ridge regression; cross-covariance operator
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Zaremba, A.; Aste, T. Measures of Causality in Complex Datasets with Application to Financial Data. Entropy 2014, 16, 2309-2349.

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