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Testing for Unit Root against LSTAR model – wavelet improvements under GARCH distortion

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  • Li, Yushu

    (CAFO, Växjö University)

  • Shukur, Ghazi

    ()
    (CESIS - Centre of Excellence for Science and Innovation Studies, Royal Institute of Technology)

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Abstract

In this paper, we propose a Nonlinear Dickey-Fuller test for unit root against first order Logistic Smooth Transition Autoregressive LSTAR (1) model with time as the transition variable. The Nonlinear Dickey-Fuller 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 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 test.

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Bibliographic Info

Paper provided by Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies in its series Working Paper Series in Economics and Institutions of Innovation with number 184.

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Length: 29 pages
Date of creation: 26 Aug 2009
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Handle: RePEc:hhs:cesisp:0184

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Postal: CESIS - Centre of Excellence for Science and Innovation Studies, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
Phone: +46 8 790 95 63
Web page: http://www.infra.kth.se/cesis/
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Keywords: Unit root Test; Dickey-Fuller test; STAR model; GARCH; Wavelet method; MODWT;

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