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Testing for Unit Root against LSTAR Model: Wavelet Improvement under GARCH Distortion

Author

Listed:
  • Li, Yushu

    (Centre for Labour Market Policy Research (CAFO))

  • Shukur, Ghazi

    (Centre for Labour Market Policy Research (CAFO))

Abstract

In this paper, we propose a Nonlinear Dickey-Fuller F test for unit root against first order Logistic Smooth Transition Autoregressive LSTAR (1) model with time as the transition variable. The Nonlinear Dickey-Fuller F test statistic is established under the null hypothesis of random walk without drift and the alternative model is a nonlinear LSTAR (1) model. The asymptotic distribution of the test is analytically derived while the small sample distributions are investigated by Monte Carlo experiment. The size and power properties of the test have been investigated using Monte Carlo experiment. The results have shown that there is a serious size distortion for the Nonlinear Dickey-Fuller F test when GARCH errors appear in the Data Generating Process (DGP), which lead to an over-rejection of the unit root null hypothesis. To solve this problem, we use the Wavelet technique to count off the GARCH distortion and to improve the size property of the test under GARCH error. We also discuss the asymptotic distributions of the test statistics in GARCH and wavelet environments. Finally, an empirical example is used to compare our test with the traditional Dickey-Fuller F test.

Suggested Citation

  • Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR Model: Wavelet Improvement under GARCH Distortion," CAFO Working Papers 2009:6, Linnaeus University, Centre for Labour Market Policy Research (CAFO), School of Business and Economics.
    • Handle: RePEc:hhs:vxcafo:2009_006
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    References listed on IDEAS

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    More about this item

    Keywords

    Unit root Test; Dickey-Fuller F test; STAR model; GARCH (1: 1) Wavelet method; MODWT;
    All these keywords.

    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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