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A New Test for Chaos and Determinism based on Symbolic Dynamics

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  • Mariano Matilla-García

    (UPCT - Universidad Politécnica de Cartagena / Technical University of Cartagena)

  • Manuel Ruiz Marín

    (UPCT - Universidad Politécnica de Cartagena / Technical University of Cartagena)

Abstract

We propose a novel test to determine, given a time series, if the dynamics are generated by a deterministic (including low dimensional chaos), rather than a stochastic, process. In addition, we introduce a new nonparametric bootstrap test for independence which is consistent against a broad class of alternatives. The conditions under which the tests can be applied are very weak. The advantages of the presented methods are simplicity, invariance with respect to monotonic transformations and the applicability of the tests regardless of the discrete or continuous nature of the data generating process. We conduct several simulation studies to evaluate the performance of our tests on well-known dynamic processes. Finally, our tests are applied to several sets of financial returns that have been recently studied.

Suggested Citation

  • Mariano Matilla-García & Manuel Ruiz Marín, 2010. "A New Test for Chaos and Determinism based on Symbolic Dynamics," Post-Print hal-00911819, HAL.
    • Handle: RePEc:hal:journl:hal-00911819
    DOI: 10.1016/j.jebo.2010.09.017
    Note: View the original document on HAL open archive server: https://hal.science/hal-00911819
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    Cited by:

    1. Lucía Inglada-Pérez & Pablo Coto-Millán, 2021. "A Chaos Analysis of the Dry Bulk Shipping Market," Mathematics, MDPI, vol. 9(17), pages 1-35, August.
    2. Miguel Henry & George Judge, 2019. "Permutation Entropy and Information Recovery in Nonlinear Dynamic Economic Time Series," Econometrics, MDPI, vol. 7(1), pages 1-16, March.
    3. Luo, Wenya & Bai, Zhidong & Zheng, Shurong & Hui, Yongchang, 2020. "A modified BDS test," Statistics & Probability Letters, Elsevier, vol. 164(C).
    4. Elsinger, Helmut, 2013. "Comment on: A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 91(C), pages 131-138.
    5. Fernando López & Mariano Matilla-García & Jesús Mur & Manuel Ruiz Marín, 2021. "Statistical Tests of Symbolic Dynamics," Mathematics, MDPI, vol. 9(8), pages 1-21, April.
    6. Mastroeni, Loretta & Vellucci, Pierluigi & Naldi, Maurizio, 2019. "A reappraisal of the chaotic paradigm for energy commodity prices," Energy Economics, Elsevier, vol. 82(C), pages 167-178.

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