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Testing for Unit Root Against LSTAR Models: Wavelet Improvement under GARCH Distortion
Department of Economic and Statistics, Center for Labor Market Policy Research (CAFO), Linaeus University, Växjö, Sweden.
Jönköping University, Jönköping International Business School, JIBS, Economics.
2010 (English)In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 39, no 2, 277-286 p.Article in journal (Refereed) Published
Abstract [en]

In this article, 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 were investigated using Monte Carlo experiment. The results showed that there is a serious size distortion for the test when GARCH errors appear in the Data Generating Process (DGP), which led 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 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.

Place, publisher, year, edition, pages
2010. Vol. 39, no 2, 277-286 p.
Keyword [en]
Dickey-Fuller F test, GARCH(1, 1), MODWT, STAR model, Unit root test, Wavelet method
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-13662DOI: 10.1080/03610910903443964OAI: oai:DiVA.org:hj-13662DiVA: diva2:359815
Available from: 2010-10-30 Created: 2010-10-30 Last updated: 2011-01-19Bibliographically approved

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Citation style
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