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A New Bispectral Test for Nonlinear Serial Dependence

Author

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  • Elena Rusticelli
  • Richard A. Ashley
  • Estela Bee Dagum
  • Douglas M. Patterson

Abstract

Nonconstancy of the bispectrum of a time series has been taken as a measure of non-Gaussianity and nonlinear serial dependence in a stochastic process by Subba Rao and Gabr (1980) and by Hinich (1982), leading to Hinich's statistical test of the null hypothesis of a linear generating mechanism for a time series. Hinich's test has the advantage of focusing directly on nonlinear serial dependence—in contrast to subsequent approaches, which actually test for serial dependence of any kind (nonlinear or linear) on data which have been pre-whitened. The Hinich test tends to have low power, however, and (in common with most statistical procedures in the frequency domain) requires the specification of a smoothing or window-width parameter. In this article, we develop a modification of the Hinich bispectral test which substantially ameliorates both of these problems by the simple expedient of maximizing the test statistic over the feasible values of the smoothing parameter. Monte Carlo simulation results are presented indicating that the new test is well sized and has substantially larger power than the original Hinich test against a number of relevant alternatives; the simulations also indicate that the new test preserves the Hinich test's robustness to misspecifications in the identification of a pre-whitening model.
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Suggested Citation

  • Elena Rusticelli & Richard A. Ashley & Estela Bee Dagum & Douglas M. Patterson, 2006. "A New Bispectral Test for Nonlinear Serial Dependence," Working Papers e06-6, Virginia Polytechnic Institute and State University, Department of Economics.
  • Handle: RePEc:vpi:wpaper:e06-6
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    File URL: http://ashleymac.econ.vt.edu/working_papers/maximal_bispectral.pdf
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    References listed on IDEAS

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    1. Barnett, William A. & Gallant, A. Ronald & Hinich, Melvin J. & Jungeilges, Jochen A. & Kaplan, Daniel T. & Jensen, Mark J., 1997. "A single-blind controlled competition among tests for nonlinearity and chaos," Journal of Econometrics, Elsevier, vol. 82(1), pages 157-192.
    2. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April.
    3. Ashley, Richard A & Patterson, Douglas M, 1989. "Linear versus Nonlinear Macroeconomies: A Statistical Test," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(3), pages 685-704, August.
    4. Pedro JF de Lima, 1996. "Nonlinearities and Nonstationarities in Stock Returns," Economics Working Paper Archive 360, The Johns Hopkins University,Department of Economics.
    5. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
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    Cited by:

    1. Mutschler, Willi, 2015. "Note on Higher-Order Statistics for the Pruned-State-Space of nonlinear DSGE models," Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 113138, Verein für Socialpolitik / German Economic Association.
    2. Harvill, Jane L. & Ravishanker, Nalini & Ray, Bonnie K., 2013. "Bispectral-based methods for clustering time series," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 113-131.
    3. Mutschler, Willi, 2015. "Identification of DSGE models—The effect of higher-order approximation and pruning," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 34-54.

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    Keywords

    Bispectrum; nonlinearity; time series analysis;

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