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Testing For Serial Correlation Of Unknown Form Using Wavelet Methods

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  • Lee, Jin
  • Hong, Yongmiao
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    Abstract

    A wavelet-based consistent test for serial correlation of unknown form is proposed. As a spatially adaptive estimation method, wavelets can effectively detect local features such as peaks and spikes in a spectral density, which can arise as a result of strong autocorrelation or seasonal or business cycle periodicities in economic and financial time series. The proposed test statistic is constructed by comparing a wavelet-based spectral density estimator and the null spectral density. It is asymptotically one-sided N(0,1) under the null hypothesis of no serial correlation and is consistent against serial correlation of unknown form. The test is expected to have better power than a kernel-based test (e.g., Hong, 1996, Econometrica 64, 837 864) when the true spectral density has significant spatial inhomogeneity. This is confirmed in a simulation study. Because the spectral densities of time series arising in practice usually have unknown smoothness, the wavelet-based test is a useful complement to the kernel-based test in practice.

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    Bibliographic Info

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

    Volume (Year): 17 (2001)
    Issue (Month): 02 (April)
    Pages: 386-423

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    Handle: RePEc:cup:etheor:v:17:y:2001:i:02:p:386-423_17

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    Cited by:
    1. Li, Yushu & Andersson, Fredrik N. G., 2014. "A simple wavelet-based test for serial correlation in panel data models," Discussion Papers 2014/11, Department of Business and Management Science, Norwegian School of Economics.
    2. Kim, Sangbae & In, Francis, 2005. "The relationship between stock returns and inflation: new evidence from wavelet analysis," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 435-444, June.
    3. Li, Linyuan & Yao, Shan & Duchesne, Pierre, 2014. "On wavelet-based testing for serial correlation of unknown form using Fan’s adaptive Neyman method," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 308-327.
    4. Peter C.B. Phillips, 2004. "Automated Discovery in Econometrics," Cowles Foundation Discussion Papers 1469, Cowles Foundation for Research in Economics, Yale University.
    5. Gencay, Ramazan & Fan, Yanqin, 2007. "Unit Root Tests with Wavelets," MPRA Paper 9832, University Library of Munich, Germany.
    6. 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.
    7. 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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