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Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors


  • Li, Yushu

    () (Centre for Labour Market Policy Research (CAFO))

  • Shukur, Ghazi

    () (Centre for Labour Market Policy Research (CAFO))


In this paper, we use the wavelet technique to improve the over-rejection problem of the traditional Dickey-Fuller test for unit root when the data suffers from GARCH (1,1) effect. The logic is based on that the wavelet spectrum decomposition can separate out information of different frequencies in the data series. We prove that the asymptotic distribution of our test is similar to the traditional Dickey-Fuller(1979 and 1981) type of tests. The small sample distribution of the new test is assessed by means of Monte Carlo simulation. An empirical example with data on immigration to Sweden during the period 1950 to 2000 is used to illustrate the test. The results reveal that using the traditional Dickey-Fuller type of test, the unit root is rejected while our wavelet improved test shows the opposite result.

Suggested Citation

  • Li, Yushu & Shukur, Ghazi, 2009. "Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors," CAFO Working Papers 2009:7, Linnaeus University, Centre for Labour Market Policy Research (CAFO), School of Business and Economics.
  • Handle: RePEc:hhs:vxcafo:2009_007

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    References listed on IDEAS

    1. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    2. Ling, Shiqing & Li, W.K., 2003. "Asymptotic Inference For Unit Root Processes With Garch(1,1) Errors," Econometric Theory, Cambridge University Press, vol. 19(4), pages 541-564, August.
    3. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
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    More about this item


    Dickey-Fuller test; GARCH (1:1); Wavelet spectrum decomposition; MODWT;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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