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Evaluation of Surrogate and Bootstrap Tests for Nonlinearity in Time Series

Author

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  • Kugiumtzis Dimitris

    (Aristotle University of Thessaloniki)

Abstract

The validity of any test for nonlinearity based on resampling techniques depends heavily on the consistency of the generated resampled data to the null hypothesis of linear stochastic process. The surrogate data generating algorithms AAFT, IAAFT and STAP, as well as a residual-based bootstrap algorithm, all used for the randomization or bootstrap test for nonlinearity, are reviewed and their performance is compared using different nonlinear statistics for the test. The simulations on linear and nonlinear stochastic systems, as well as chaotic systems, reveals a variation in the test outcome with the algorithm and statistic. Overall, the bootstrap algorithm led to smallest test power whereas the STAP algorithm gave consistently good results in terms of size and power of the test. The performance of the nonlinearity test with the resampling techniques is evaluated on volume and return time series of international stock exchange indices.

Suggested Citation

  • 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.
    • Handle: RePEc:bpj:sndecm:v:12:y:2008:i:1:n:4
    DOI: 10.2202/1558-3708.1474
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    1. Kugiumtzis, Dimitris & Tsimpiris, Alkiviadis, 2010. "Measures of Analysis of Time Series (MATS): A MATLAB Toolkit for Computation of Multiple Measures on Time Series Data Bases," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i05).
    2. Li Wang & Xing-Lu Gao & Wei-Xing Zhou, 2023. "Testing for intrinsic multifractality in the global grain spot market indices: A multifractal detrended fluctuation analysis," Papers 2306.10496, arXiv.org.
    3. Benbachir, Saâd & El Alaoui, Marwane, 2011. "A Multifractal Detrended Fluctuation Analysis of the Moroccan Stock Exchange," MPRA Paper 49003, University Library of Munich, Germany.
    4. Petre CARAIANI, 2015. "Testing For Nonlinearity In Unemployment Rates Via Delay Vector Variance," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 81-92, March.
    5. Papapetrou, M. & Kugiumtzis, D., 2013. "Markov chain order estimation with conditional mutual information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1593-1601.
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    7. El Alaoui, Marwane, 2017. "Price–volume multifractal analysis of the Moroccan stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 473-485.
    8. John Halley & Dimitris Kugiumtzis, 2011. "Nonparametric testing of variability and trend in some climatic records," Climatic Change, Springer, vol. 109(3), pages 549-568, December.

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