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

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  • Li, Yushu

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

  • Shukur, Ghazi

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

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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.

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Bibliographic Info

Paper provided by Centre for Labour Market Policy Research (CAFO), School of Business and Economics, Linnaeus University in its series CAFO Working Papers with number 2009:6.

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Length: 27 pages
Date of creation: 26 Feb 2009
Date of revision:
Handle: RePEc:hhs:vxcafo:2009_006

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Postal: Centre for Labour Market Policy Research (CAFO), School of Business and Economics, Linnaeus University, SE 351 95 Växjö, Sweden
Phone: +46 470 70 87 64
Web page: http://lnu.se/research-groups/cafo?l=en
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Keywords: Unit root Test; Dickey-Fuller F test; STAR model; GARCH (1: 1) Wavelet method; MODWT;

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