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Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models

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  • Yongmiao Hong
  • Chihwa Kao

Abstract

Wavelet analysis is a new mathematical method developed as a unified field of science over the last decade or so. As a spatially adaptive analytic tool, wavelets are useful for capturing serial correlation where the spectrum has peaks or kinks, as can arise from persistent dependence, seasonality, and other kinds of periodicity. This paper proposes a new class of generally applicable wavelet-based tests for serial correlation of unknown form in the estimated residuals of a panel regression model, where error components can be one-way or two-way, individual and time effects can be fixed or random, and regressors may contain lagged dependent variables or deterministic/stochastic trending variables. Our tests are applicable to unbalanced heterogenous panel data. They have a convenient null limit N(0,1) distribution. No formulation of an alternative model is required, and our tests are consistent against serial correlation of unknown form even in the presence of substantial inhomogeneity in serial correlation across individuals. This is in contrast to existing serial correlation tests for panel models, which ignore inhomogeneity in serial correlation across individuals by assuming a common alternative, and thus have no power against the alternatives where the average of serial correlations among individuals is close to zero. We propose and justify a data-driven method to choose the smoothing parameter-the finest scale in wavelet spectral estimation, making the tests completely operational in practice. The data-driven finest scale automatically converges to zero under the null hypothesis of no serial correlation and diverges to infinity as the sample size increases under the alternative, ensuring the consistency of our tests. Simulation shows that our tests perform well in small and finite samples relative to some existing tests. Copyright The Econometric Society 2004.

Suggested Citation

  • Yongmiao Hong & Chihwa Kao, 2004. "Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models," Econometrica, Econometric Society, vol. 72(5), pages 1519-1563, September.
  • Handle: RePEc:ecm:emetrp:v:72:y:2004:i:5:p:1519-1563
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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00542.x
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    Cited by:

    1. Viviana Fernandez, 2005. "Time-Scale Decomposition of Price Transmission in International Markets," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 41(4), pages 57-90, August.
    2. Wu, Jianhong & Zhu, Lixing, 2011. "Testing for serial correlation and random effects in a two-way error component regression model," Economic Modelling, Elsevier, vol. 28(6), pages 2377-2386.
    3. Okui, Ryo, 2009. "Testing serial correlation in fixed effects regression models based on asymptotically unbiased autocorrelation estimators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(9), pages 2897-2909.
    4. Li, Yushu & Andersson, Fredrik N. G., 2013. "A Simple Wavelet-Based Test for Serial Correlation in Panel Data Models," Working Papers 2013:39, Lund University, Department of Economics.
    5. Michis, Antonis A., 2014. "Time scale evaluation of economic forecasts," Economics Letters, Elsevier, vol. 123(3), pages 279-281.
    6. 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.
    7. Viviana Fernández & Ali M. Kutan, 2005. "Do Regional Integration Agreements Increase Business-Cycle Convergence? Evidence from Apec and Nafta," Documentos de Trabajo 202, Centro de Economía Aplicada, Universidad de Chile.
    8. Viviana Fernandez, 2005. "Time-Scale Decomposition of Price Transmission in International Markets," Emerging Markets Finance and Trade, M.E. Sharpe, Inc., vol. 41(4), pages 57-90, August.
    9. Gonçalo Faria & Fabio Verona, 2017. "Forecasting stock market returns by summing the frequency-decomposed parts," CEF.UP Working Papers 1702, Universidade do Porto, Faculdade de Economia do Porto.
    10. Baltagi, Badi H. & Jung, Byoung Cheol & Song, Seuck Heun, 2010. "Testing for heteroskedasticity and serial correlation in a random effects panel data model," Journal of Econometrics, Elsevier, vol. 154(2), pages 122-124, February.
    11. Fernandez, Viviana, 2006. "Does domestic cooperation lead to business-cycle convergence and financial linkages?," The Quarterly Review of Economics and Finance, Elsevier, vol. 46(3), pages 369-396, July.
    12. Gao, Jiti & Hong, Yongmiao, 2007. "Central limit theorems for weighted quadratic forms of dependent processes with applications in specification testing," MPRA Paper 11977, University Library of Munich, Germany, revised Dec 2007.
    13. Viviana Fernandez, 2008. "Traditional versus novel forecasting techniques: how much do we gain?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(7), pages 637-648.
    14. Haven, Emmanuel & Liu, Xiaoquan & Shen, Liya, 2012. "De-noising option prices with the wavelet method," European Journal of Operational Research, Elsevier, vol. 222(1), pages 104-112.
    15. Gençay, Ramazan & Signori, Daniele, 2015. "Multi-scale tests for serial correlation," Journal of Econometrics, Elsevier, vol. 184(1), pages 62-80.
    16. Fernandez, Viviana, 2006. "The CAPM and value at risk at different time-scales," International Review of Financial Analysis, Elsevier, vol. 15(3), pages 203-219.
    17. Du, Zaichao, 2014. "Testing for serial independence of panel errors," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 248-261.
    18. Ramazan Gencay & Nikola Gradojevic, 2009. "Errors-in-Variables Estimation with No Instruments," Working Paper series 30_09, Rimini Centre for Economic Analysis.
    19. Thomas Conlon & John Cotter & Ramazan Gençay, 2015. "Long-run international diversification," Working Papers 201502, Geary Institute, University College Dublin.
    20. 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.
    21. 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.
    22. Sun, Edward W. & Chen, Yi-Ting & Yu, Min-Teh, 2015. "Generalized optimal wavelet decomposing algorithm for big financial data," International Journal of Production Economics, Elsevier, vol. 165(C), pages 194-214.

    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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