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On Testing For Serial Correlation With A Wavelet-Based Spectral Density Estimator In Multivariate Time Series


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  • Duchesne, Pierre


A new one-sided test for serial correlation in multivariate time series models is proposed. The test is based on a comparison between a multivariate spectral density estimator and the spectral density under the null hypothesis of no serial correlation. Duchesne and Roy (2004, Journal of Multivariate Analysis 89, 148 180) considered a multivariate kernel-based spectral density estimator. However, when the spectral density exhibits irregular features (because of strong autocorrelation or seasonality, among other factors), it is expected that a multivariate wavelet-based spectral density estimator will capture more effectively the local behavior of the spectral density. We consider a test based on a wavelet spectral density estimator, which represents a generalization of a test proposed by Lee and Hong (2001, Econometric Theory 17, 386 423). The asymptotic distribution of the new test is established under the null hypothesis, which is N(0,1). We propose and justify a suitable data-driven method to choose the smoothing parameter of the wavelet estimator (called the finest scale in that context). The new test should be powerful when the spectral density contains peaks or bumps. This is confirmed in a simulation study, where kernel-based and wavelet-based estimators are compared.The author thanks the co-editor Pentti Saikkonen and two referees for their constructive remarks and suggestions. Many thoughtful comments of the referees led to significant improvements of the paper. This work was supported by grants from the National Science and Engineering Research Council of Canada and the Fonds qu b cois de la recherche sur la nature et les technologies du Qu bec (Canada).

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 22 (2006)
Issue (Month): 04 (August)
Pages: 633-676

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Handle: RePEc:cup:etheor:v:22:y:2006:i:04:p:633-676_06

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Cited by:
  1. Peter C.B. Phillips, 2004. "Automated Discovery in Econometrics," Cowles Foundation Discussion Papers 1469, Cowles Foundation for Research in Economics, Yale University.
  2. Duchesne, Pierre, 2006. "Testing for multivariate autoregressive conditional heteroskedasticity using wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2142-2163, December.
  3. Duchesne, Pierre & Li, Linyuan & Vandermeerschen, Jill, 2010. "On testing for serial correlation of unknown form using wavelet thresholding," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2512-2531, November.
  4. Gencay, Ramazan & Fan, Yanqin, 2007. "Unit Root Tests with Wavelets," MPRA Paper 9832, University Library of Munich, Germany.
  5. Zhou, Yong & Wan, Alan T.K. & Xie, Shangyu & Wang, Xiaojing, 2010. "Wavelet analysis of change-points in a non-parametric regression with heteroscedastic variance," Journal of Econometrics, Elsevier, vol. 159(1), pages 183-201, November.


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