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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. Deo, Rohit S., 2000. "Spectral tests of the martingale hypothesis under conditional heteroscedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 99(2), pages 291-315, December.
  2. Kani Chen & Zhiliang Ying & Hong Zhang & Lincheng Zhao, 2008. "Analysis of least absolute deviation," Biometrika, Biometrika Trust, Biometrika Trust, vol. 95(1), pages 107-122.
  3. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, Econometric Society, vol. 64(4), pages 837-64, July.
  4. Miguel A. Delgado & Javier Hidalgo & Carlos Velasco, 2005. "Distribution Free Goodness-of-Fit Tests for Linear Processes," STICERD - Econometrics Paper Series, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE /2005/482, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. 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, Elsevier, vol. 133(2), pages 841-862, August.
  6. Juan Carlos Escanciano, 2005. "Goodness-of-fit Tests for Linear and Non-linear Time Series Models," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 02/05, School of Economics and Business Administration, University of Navarra.
  7. J. Carlos Escanciano & Carlos Velasco, 2003. "Generalized Spectral Tests For The Martingale Difference Hypothesis," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws035212, Universidad Carlos III, Departamento de Estadística y Econometría.
  8. Shao, Xiaofeng, 2011. "Testing For White Noise Under Unknown Dependence And Its Applications To Diagnostic Checking For Time Series Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 27(02), pages 312-343, April.
  9. Steven N. Durlauf, 1992. "Spectral Based Testing of the Martingale Hypothesis," NBER Technical Working Papers, National Bureau of Economic Research, Inc 0090, National Bureau of Economic Research, Inc.
  10. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 18(01), pages 17-39, February.
  11. Lobato I. N., 2001. "Testing That a Dependent Process Is Uncorrelated," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 96, pages 1066-1076, September.
  12. Shao, Xiaofeng, 2011. "A bootstrap-assisted spectral test of white noise under unknown dependence," Journal of Econometrics, Elsevier, Elsevier, vol. 162(2), pages 213-224, June.
  13. Chen, Kani & Guo, Shaojun & Lin, Yuanyuan & Ying, Zhiliang, 2010. "Least Absolute Relative Error Estimation," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 105(491), pages 1104-1112.
  14. Delgado, Miguel A. & Velasco, Carlos, 2011. "An Asymptotically Pivotal Transform of the Residuals Sample Autocorrelations With Application to Model Checking," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 106(495), pages 946-958.
  15. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 19(02), pages 280-310, April.
  16. 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, Taylor & Francis Journals, vol. 31(4), pages 426-437, October.
  17. Ling, Shiqing, 2007. "Self-weighted and local quasi-maximum likelihood estimators for ARMA-GARCH/IGARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 140(2), pages 849-873, October.
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