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A random-projection based test of Gaussianity for stationary processes

Author

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  • Nieto-Reyes, Alicia
  • Cuesta-Albertos, Juan Antonio
  • Gamboa, Fabrice

Abstract

Gaussianity tests have being widely studied in the literature. Regarding the study of Gaussianity tests for stationary processes, these only verify the Gaussianity of a marginal at a fixed finite order, generally order one. Therefore, they do not reject stationary non-Gaussian processes with the one-dimensional Gaussian marginal. Thus, a consistent test is proposed for Gaussianity of stationary processes when a finite sample path of the process is observed. Using random projections, decision rules are applied to the whole distribution of the process and not only on its marginal distribution at a fixed order, as in previous tests. The main idea is to test the Gaussianity of the one-dimensional marginal distribution of some random linear transformations of the process. Note that testing the one-dimensional marginal distribution can be done with previous tests of Gaussianity for stationary processes. It is shown by both theoretical and empirical studies that the proposed test procedure has good properties for a wide range of alternatives.

Suggested Citation

  • Nieto-Reyes, Alicia & Cuesta-Albertos, Juan Antonio & Gamboa, Fabrice, 2014. "A random-projection based test of Gaussianity for stationary processes," Computational Statistics & Data Analysis, Elsevier, vol. 75(C), pages 124-141.
    • Handle: RePEc:eee:csdana:v:75:y:2014:i:c:p:124-141
    DOI: 10.1016/j.csda.2014.01.013
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    References listed on IDEAS

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    1. Lobato, Ignacio N. & Velasco, Carlos, 2004. "A Simple Test Of Normality For Time Series," Econometric Theory, Cambridge University Press, vol. 20(4), pages 671-689, August.
    2. Fang, Kai-Tai & Li, Run-Ze & Liang, Jia-Juan, 1998. "A multivariate version of Ghosh's T3-plot to detect non-multinormality," Computational Statistics & Data Analysis, Elsevier, vol. 28(4), pages 371-386, October.
    3. Kavalieris, Laimonis, 2008. "Uniform convergence of autocovariances," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 830-838, April.
    4. Cuesta-Albertos, J.A. & del Barrio, E. & Fraiman, R. & Matran, C., 2007. "The random projection method in goodness of fit for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4814-4831, June.
    5. T. Subba Rao & M. M. Gabr, 1980. "A Test For Linearity Of Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(2), pages 145-158, March.
    6. Liu, Shen & Maharaj, Elizabeth Ann, 2013. "A hypothesis test using bias-adjusted AR estimators for classifying time series in small samples," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 32-49.
    7. Cuesta, Juan Antonio & Matrán, Carlos, 1991. "On the asymptotic behavior of sums of pairwise independent random variables," Statistics & Probability Letters, Elsevier, vol. 11(3), pages 201-210, March.
    8. Cuesta-Albertos, J.A. & Nieto-Reyes, A., 2008. "The random Tukey depth," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4979-4988, July.
    9. Cuesta, Juan Antonio & Matrán, Carlos, 1991. "On the asymptotic behavior of sums of pairwise independent random variables," Statistics & Probability Letters, Elsevier, vol. 12(2), pages 183-183, August.
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