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Open AccessArticle

Measures of Causality in Complex Datasets with Application to Financial Data

by 1,* and 1,2
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.
Entropy 2014, 16(4), 2309-2349; https://doi.org/10.3390/e16042309
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)
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
MDPI and ACS Style

Zaremba, A.; Aste, T. Measures of Causality in Complex Datasets with Application to Financial Data. Entropy 2014, 16, 2309-2349. https://doi.org/10.3390/e16042309

AMA Style

Zaremba A, Aste T. Measures of Causality in Complex Datasets with Application to Financial Data. Entropy. 2014; 16(4):2309-2349. https://doi.org/10.3390/e16042309

Chicago/Turabian Style

Zaremba, Anna; Aste, Tomaso. 2014. "Measures of Causality in Complex Datasets with Application to Financial Data" Entropy 16, no. 4: 2309-2349. https://doi.org/10.3390/e16042309

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