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A bootstrap-assisted spectral test of white noise under unknown dependence

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  • Shao, Xiaofeng

Abstract

To test for the white noise null hypothesis, we study the Cramér-von Mises test statistic that is based on the sample spectral distribution function. Since the critical values of the test statistic are difficult to obtain, we propose a blockwise wild bootstrap procedure to approximate its asymptotic null distribution. Using a Hilbert space approach, we establish the weak convergence of the difference between the sample spectral distribution function and the true spectral distribution function, as well as the consistency of bootstrap approximation under mild assumptions. Finite sample results from a simulation study and an empirical data analysis are also reported.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 162 (2011)
Issue (Month): 2 (June)
Pages: 213-224

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Handle: RePEc:eee:econom:v:162:y:2011:i:2:p:213-224

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Hypothesis testing Spectral distribution function Time series White noise Wild bootstrap;

References

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  1. J. Carlos Escanciano & Carlos Velasco, 2003. "Generalized Spectral Tests For The Martingale Difference Hypothesis," Statistics and Econometrics Working Papers ws035212, Universidad Carlos III, Departamento de Estadística y Econometría.
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  14. Horowitz, Joel L. & Lobato, I.N. & Nankervis, John C. & Savin, N.E., 2006. "Bootstrapping the Box-Pierce Q test: A robust test of uncorrelatedness," Journal of Econometrics, Elsevier, vol. 133(2), pages 841-862, August.
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Citations

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Cited by:
  1. Guay, Alain & Guerre, Emmanuel & Lazarová, Štěpána, 2013. "Robust adaptive rate-optimal testing for the white noise hypothesis," Journal of Econometrics, Elsevier, vol. 176(2), pages 134-145.
  2. Zhu, Ke & Li, Wai-Keung, 2013. "A bootstrapped spectral test for adequacy in weak ARMA models," MPRA Paper 51224, University Library of Munich, Germany.
  3. Doukhan, Paul & Lang, Gabriel & Leucht, Anne & Neumann, Michael H., 2014. "Dependent wild bootstrap for the empirical process," Working Papers 35246, University of Mannheim, Department of Economics.
  4. Chen, Min & Zhu, Ke, 2014. "Sign-based specification tests for martingale difference with conditional heteroscedasity," MPRA Paper 56347, University Library of Munich, Germany.

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