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A New Bispectral Test for NonLinear Serial Dependence

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  • Elena Rusticelli
  • Richard Ashley
  • Estela Bee Dagum
  • Douglas 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.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:28:y:2009:i:1-3:p:279-293
    DOI: 10.1080/07474930802388090
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    References listed on IDEAS

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    1. Pedro JF de Lima, 1996. "Nonlinearities and Nonstationarities in Stock Returns," Economics Working Paper Archive 360, The Johns Hopkins University,Department of Economics.
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    Cited by:

    1. 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.
    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.

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    1. 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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