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Tests for Serial Independence and Linearity Based on Correlation Integrals

Author

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  • Diks Cees

    (CeNDEF - University of Amsterdam)

  • Manzan Sebastiano

    (CeNDEF - University of Amsterdam)

Abstract

We propose information theoretic tests for serial independence and linearity in time series against nonlinear dependence on lagged variables, based on the conditional mutual information. The conditional mutual information, which is a general measure for dependence, is estimated using the correlation integral from chaos theory. The significance of the test statistics is determined by means of bootstrap methods. The size and power properties of the tests are examined by simulation and illustrated with applications to real US GNP data.

Suggested Citation

  • Diks Cees & Manzan Sebastiano, 2002. "Tests for Serial Independence and Linearity Based on Correlation Integrals," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(2), pages 1-22, July.
  • Handle: RePEc:bpj:sndecm:v:6:y:2002:i:2:n:2
    DOI: 10.2202/1558-3708.1005
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    References listed on IDEAS

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    1. Aparicio F. M. & Escribano A., 1998. "Information-Theoretic Analysis of Serial Dependence and Cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(3), pages 1-24, October.
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    10. Diks, C.G.H., 1999. "Consistent Testing for Serial Independence," CeNDEF Working Papers 99-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    11. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Lag Selection for Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 457-487, July.
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    Cited by:

    1. João Henrique Gonçalves Mazzeu & Esther Ruiz & Helena Veiga, 2018. "Uncertainty And Density Forecasts Of Arma Models: Comparison Of Asymptotic, Bayesian, And Bootstrap Procedures," Journal of Economic Surveys, Wiley Blackwell, vol. 32(2), pages 388-419, April.
    2. Diks Cees & Panchenko Valentyn, 2008. "Rank-based Entropy Tests for Serial Independence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-21, March.
    3. Lanh Tran & Ba Chu & Chunfeng Huang & Kim P. Huynh, 2014. "Adaptive permutation tests for serial independence," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 183-208, August.
    4. Angeliki Papana & Catherine Kyrtsou & Dimitris Kugiumtzis & Cees Diks, 2017. "Assessment of resampling methods for causality testing: A note on the US inflation behavior," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-20, July.
    5. Papadopoulos, G. & Kugiumtzis, D., 2015. "Estimation of connectivity measures in gappy time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 387-398.
    6. Gao, Wei & Zhao, Hongxia, 2013. "Conditional independence graph for nonlinear time series and its application to international financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(10), pages 2460-2469.
    7. Kugiumtzis Dimitris, 2008. "Evaluation of Surrogate and Bootstrap Tests for Nonlinearity in Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-26, March.

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