Scandinavian Working Papers in Economics

CAFO Working Papers,
Linnaeus University, Centre for Labour Market Policy Research (CAFO), School of Business and Economics

No 2009:6: Testing for Unit Root against LSTAR Model: Wavelet Improvement under GARCH Distortion

Yushu Li () and Ghazi Shukur ()
Additional contact information
Yushu Li: Centre for Labour Market Policy Research (CAFO), Postal: Centre for Labour Market Policy Research (CAFO), Dept of Economics and Statistics, School of Management and Economics, Växjö University , SE 351 95 Växjö, Sweden
Ghazi Shukur: Centre for Labour Market Policy Research (CAFO), Postal: Centre for Labour Market Policy Research (CAFO), Dept of Economics and Statistics, School of Management and Economics, Växjö University , SE 351 95 Växjö, Sweden

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.

Keywords: Unit root Test; Dickey-Fuller F test; STAR model; GARCH (1: 1) Wavelet method; MODWT

JEL-codes: C15; C52

27 pages, February 26, 2009

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