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Measures of Causality in Complex Datasets with application to financial data

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  • Anna Zaremba
  • Tomaso Aste

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.

Suggested Citation

  • Anna Zaremba & Tomaso Aste, 2014. "Measures of Causality in Complex Datasets with application to financial data," Papers 1401.1457, arXiv.org, revised Jun 2014.
    • Handle: RePEc:arx:papers:1401.1457
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    References listed on IDEAS

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    1. Hsiao, Cheng, 1982. "Autoregressive modeling and causal ordering of economic variables," Journal of Economic Dynamics and Control, Elsevier, vol. 4(1), pages 243-259, November.
    2. Abdulnasser Hatemi-J, 2012. "Asymmetric causality tests with an application," Empirical Economics, Springer, vol. 43(1), pages 447-456, August.
    3. Eichler, Michael, 2007. "Granger causality and path diagrams for multivariate time series," Journal of Econometrics, Elsevier, vol. 137(2), pages 334-353, April.
    4. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
    5. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
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    Cited by:

    1. Tomaso Aste & T. Di Matteo, 2017. "Sparse Causality Network Retrieval from Short Time Series," Complexity, Hindawi, vol. 2017, pages 1-13, November.
    2. Civitarese, Jamil, 2016. "Volatility and correlation-based systemic risk measures in the US market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 459(C), pages 55-67.
    3. Anna B. Zaremba & Gareth W. Peters, 2022. "Statistical Causality for Multivariate Nonlinear Time Series via Gaussian Process Models," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2587-2632, December.
    4. Kuang, Peng-Cheng, 2021. "Measuring information flow among international stock markets: An approach of entropy-based networks on multi time-scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 577(C).

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