Testing for Unit Root against LSTAR Model: Wavelet Improvement under GARCH Distortion
AbstractIn 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 InfoPaper 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.
Length: 27 pages
Date of creation: 26 Feb 2009
Date of revision:
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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
More information through EDIRC
Unit root Test; Dickey-Fuller F test; STAR model; GARCH (1: 1) Wavelet method; MODWT;
Other versions of this item:
- Li, Yushu & Shukur, Ghazi, 2009. "Testing for Unit Root against LSTAR model – wavelet improvements under GARCH distortion," Working Paper Series in Economics and Institutions of Innovation 184, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-03-07 (All new papers)
- NEP-ECM-2009-03-07 (Econometrics)
- NEP-ETS-2009-03-07 (Econometric Time Series)
- NEP-ORE-2009-03-07 (Operations Research)
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