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Statistical Causality for Multivariate Nonlinear Time Series via Gaussian Process Models

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  • Anna B. Zaremba

    (University College London)

  • Gareth W. Peters

    (University of California Santa Barbara)

Abstract

The ability to test for statistical causality in linear and nonlinear contexts, in stationary or non-stationary settings, and to identify whether statistical causality influences trend of volatility forms a particularly important class of problems to explore in multi-modal and multivariate processes. In this paper, we develop novel testing frameworks for statistical causality in general classes of multivariate nonlinear time series models. Our framework accommodates flexible features where causality may be present in either: trend, volatility or both structural components of the general multivariate Markov processes under study. In addition, we accommodate the added possibilities of flexible structural features such as long memory and persistence in the multivariate processes when applying our semi-parametric approach to causality detection. We design a calibration procedure and formal testing procedure to detect these relationships through classes of Gaussian process models. We provide a generic framework which can be applied to a wide range of problems, including partially observed generalised diffusions or general multivariate linear or nonlinear time series models. We demonstrate several illustrative examples of features that are easily testable under our framework to study the properties of the inference procedure developed including the power of the test, sensitivity and robustness. We then illustrate our method on an interesting real data example from commodity modelling.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:4:d:10.1007_s11009-022-09928-3
    DOI: 10.1007/s11009-022-09928-3
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    References listed on IDEAS

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    1. Billio, Monica & Getmansky, Mila & Lo, Andrew W. & Pelizzon, Loriana, 2012. "Econometric measures of connectedness and systemic risk in the finance and insurance sectors," Journal of Financial Economics, Elsevier, vol. 104(3), pages 535-559.
    2. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    3. John Y. Campbell & Robert J. Shiller, 1988. "Stock Prices, Earnings and Expected Dividends," Cowles Foundation Discussion Papers 858, Cowles Foundation for Research in Economics, Yale University.
    4. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    5. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    6. Campbell, John Y & Shiller, Robert J, 1988. " Stock Prices, Earnings, and Expected Dividends," Journal of Finance, American Finance Association, vol. 43(3), pages 661-676, July.
    7. repec:pri:cepsud:91malkiel is not listed on IDEAS
    8. Wen-Den Chen, 2006. "Estimating the long memory granger causality effect with a spectrum estimator," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(3), pages 193-200.
    9. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    10. James G. MacKinnon, 1983. "Model Specification Tests Against Non-Nested Alternatives," Working Paper 573, Economics Department, Queen's University.
    11. Wilson, Paul, 2015. "The misuse of the Vuong test for non-nested models to test for zero-inflation," Economics Letters, Elsevier, vol. 127(C), pages 51-53.
    12. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    13. Anna Zaremba & Tomaso Aste, 2014. "Measures of Causality in Complex Datasets with application to financial data," Papers 1401.1457, arXiv.org, revised Jun 2014.
    14. M. A. H. Dempster & Elena Medova & Ke Tang, 2012. "Determinants of oil futures prices and convenience yields," Quantitative Finance, Taylor & Francis Journals, vol. 12(12), pages 1795-1809, December.
    15. Pearl Judea, 2010. "An Introduction to Causal Inference," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-62, February.
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