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A bootstrapped spectral test for adequacy in weak ARMA models

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  • Zhu, Ke
  • Li, Wai-Keung
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Abstract

This paper proposes a Cramer-von Mises (CM) test statistic to check the adequacy of weak ARMA models. Without posing a martingale difference assumption on the error terms, the asymptotic null distribution of the CM test is obtained by using the Hillbert space approach. Moreover, this CM test is consistent, and has nontrivial power against the local alternative of order $n^{-1/2}$. Due to the unknown dependence of error terms and the estimation effects, a new block-wise random weighting method is constructed to bootstrap the critical values of the test statistic. The new method is easy to implement and its validity is justified. The theory is illustrated by a small simulation study and an application to S\&P 500 stock index.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 51224.

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Date of creation: 06 Nov 2013
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Handle: RePEc:pra:mprapa:51224

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Keywords: Block-wise random weighting method; Diagnostic checking; Least squares estimation; Spectral test; Weak ARMA models; Wild bootstrap.;

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  1. Escanciano, J. Carlos, 2006. "Goodness-of-Fit Tests for Linear and Nonlinear Time Series Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 531-541, June.
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  3. Juan Carlos Escanciano & Ignacio N. Lobato & Lin Zhu, 2013. "Automatic Specification Testing for Vector Autoregressions and Multivariate Nonlinear Time Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(4), pages 426-437, October.
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  13. 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.
  14. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  15. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
  16. 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.
  17. Kani Chen & Zhiliang Ying & Hong Zhang & Lincheng Zhao, 2008. "Analysis of least absolute deviation," Biometrika, Biometrika Trust, vol. 95(1), pages 107-122.
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