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Testing For Serial Correlation Of Unknown Form Using Wavelet Methods

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  • Lee, Jin
  • Hong, Yongmiao

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.

Suggested Citation

  • Lee, Jin & Hong, Yongmiao, 2001. "Testing For Serial Correlation Of Unknown Form Using Wavelet Methods," Econometric Theory, Cambridge University Press, vol. 17(2), pages 386-423, April.
  • Handle: RePEc:cup:etheor:v:17:y:2001:i:02:p:386-423_17
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    Cited by:

    1. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
    2. Mengya Liu & Fukan Zhu & Ke Zhu, 2020. "Multi-frequency-band tests for white noise under heteroskedasticity," Papers 2004.09161, arXiv.org.
    3. Antonio Cosma & Olivier Scaillet & Rainer von Sachs, 2005. "Multiariate Wavelet-based sahpe preserving estimation for dependant observation," FAME Research Paper Series rp144, International Center for Financial Asset Management and Engineering.
    4. Yushu Li & Fredrik N. G. Andersson, 2021. "A simple wavelet-based test for serial correlation in panel data models," Empirical Economics, Springer, vol. 60(5), pages 2351-2363, May.
    5. 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.
    6. Phillips, Peter C.B., 2005. "Automated Discovery In Econometrics," Econometric Theory, Cambridge University Press, vol. 21(1), pages 3-20, February.
    7. Ke Zhu, 2016. "Bootstrapping the portmanteau tests in weak auto-regressive moving average models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 463-485, March.
    8. 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.
    9. Li, Linyuan & Duchesne, Pierre & Liou, Chu Pheuil, 2021. "On diagnostic checking in ARMA models with conditionally heteroscedastic martingale difference using wavelet methods," Econometrics and Statistics, Elsevier, vol. 19(C), pages 169-187.
    10. 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.
    11. Fabio S. Dias & Gareth W. Peters, 2020. "A Non-parametric Test and Predictive Model for Signed Path Dependence," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 461-498, August.
    12. Francis In & Sangbae Kim, 2012. "An Introduction to Wavelet Theory in Finance:A Wavelet Multiscale Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8431, December.
    13. Yousefi, Shahriar & Weinreich, Ilona & Reinarz, Dominik, 2005. "Wavelet-based prediction of oil prices," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 265-275.
    14. Gençay, Ramazan & Signori, Daniele, 2015. "Multi-scale tests for serial correlation," Journal of Econometrics, Elsevier, vol. 184(1), pages 62-80.
    15. Christian M. Hafner, 2012. "Cross-correlating wavelet coefficients with applications to high-frequency financial time series," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(6), pages 1363-1379, December.
    16. Ramazan Gencay & Nikola Gradojevic, 2009. "Errors-in-Variables Estimation with No Instruments," Working Paper series 30_09, Rimini Centre for Economic Analysis.
    17. Xiao, Han & Wu, Wei Biao, 2019. "Portmanteau Test and Simultaneous Inference for Serial Covariances," IRTG 1792 Discussion Papers 2019-017, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    18. Stelios Bekiros, 2014. "Timescale Analysis with an Entropy-Based Shift-Invariant Discrete Wavelet Transform," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 231-251, August.
    19. 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.
    20. Sharif Md. Raihan & Yi Wen & Bing Zeng, 2005. "Wavelet: a new tool for business cycle analysis," Working Papers 2005-050, Federal Reserve Bank of St. Louis.

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