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Entropy testing for nonlinear serial dependence in time series

Author

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  • Simone Giannerini
  • Esfandiar Maasoumi
  • Estela Bee Dagum

Abstract

We propose tests for nonlinear serial dependence in time series under the null hypothesis of general linear dependence, in contrast to the more widely studied null hypothesis of independence. The approach is based on combining an entropy dependence metric, which possesses many desirable properties and is used as a test statistic, with a suitable extension of surrogate data methods, a class of Monte Carlo distribution-free tests for nonlinearity, and a smoothed sieve bootstrap scheme. We show how, in the same way as the autocorrelation function is used for linear models, our tests can in principle be employed to detect the lags at which a significant nonlinear relationship is present. We prove the asymptotic validity of the proposed procedures and the corresponding inferences. The small-sample performance of the tests in terms of power and size is assessed through a simulation study. Applications to real datasets of different kinds are also presented.

Suggested Citation

  • Simone Giannerini & Esfandiar Maasoumi & Estela Bee Dagum, 2015. "Entropy testing for nonlinear serial dependence in time series," Biometrika, Biometrika Trust, vol. 102(3), pages 661-675.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:3:p:661-675.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv007
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    References listed on IDEAS

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    1. Esfandiar Maasoumi & Jeffrey Racine, 2009. "A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 246-261.
    2. Elena Rusticelli & Richard Ashley & Estela Bee Dagum & Douglas Patterson, 2009. "A New Bispectral Test for NonLinear Serial Dependence," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 279-293.
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    Cited by:

    1. Omane-Adjepong, Maurice & Alagidede, Imhotep Paul, 2020. "High- and low-level chaos in the time and frequency market returns of leading cryptocurrencies and emerging assets," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Zacharias Psaradakis & Marián Vávra, 2019. "Portmanteau tests for linearity of stationary time series," Econometric Reviews, Taylor & Francis Journals, vol. 38(2), pages 248-262, February.
    3. Simone Giannerini & Greta Goracci, 2023. "Entropy-Based Tests for Complex Dependence in Economic and Financial Time Series with the R Package tseriesEntropy," Mathematics, MDPI, vol. 11(3), pages 1-27, February.
    4. Lei Jiang & Esfandiar Maasoumi & Jiening Pan & Ke Wu, 2018. "A test of general asymmetric dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(7), pages 1026-1043, November.
    5. Kung-Sik Chan & Simone Giannerini & Greta Goracci & Howell Tong, 2020. "Testing for threshold regulation in presence of measurement error with an application to the PPP hypothesis," Papers 2002.09968, arXiv.org, revised Nov 2021.
    6. Renée Fry-McKibbin & Cody Yu-Ling Hsiao & Vance L. Martin, 2018. "Measuring financial interdependence in asset returns with an application to euro zone equities," CAMA Working Papers 2018-05, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    7. Marian Vavra, 2016. "Testing the Validity of Assumptions of UC-ARIMA Models for Trend-Cycle Decompositions," Working and Discussion Papers WP 4/2016, Research Department, National Bank of Slovakia.
    8. Greta Goracci & Simone Giannerini & Kung-Sik Chan & Howell Tong, 2021. "Testing for threshold effects in the TARMA framework," Papers 2103.13977, arXiv.org.

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