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Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors: An Application to Swedish Immigration Data
Department of Economic and Statistics, Center for Labor Market Policy Research (CAFO), Linnaeus University, Sweden .
Jönköping University, Jönköping International Business School, JIBS, Economics. (Statistik)
2011 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 40, no 13, 2385-2396 p.Article in journal (Refereed) Published
Abstract [en]

In this article, we use the wavelet technique to improve the over-rejection problem of the traditional Dickey-Fuller tests for unit root when the data is associated with volatility like the GARCH(1, 1) effect. The logic of this technique is based on the idea that the wavelet spectrum decomposition can separate out information of different frequencies in the data series. We prove that the asymptotic distribution of the test in the wavelet environment is still the same as the traditional Dickey-Fuller type of tests. The finite sample property is improved when the data suffers from GARCH error. The investigation of the size property and the finite sample distribution of the test is carried out by Monte Carlo experiment. An empirical example with data on the net immigration to Sweden during the period 1950-2000 is used to illustrate the performance of the wavelet improved test under GARCH errors. The results reveal that using the traditional Dickey-Fuller type of tests, the unit root hypothesis is rejected while our wavelet improved test do not reject as it is more robust to GARCH errors in finite samples.

Place, publisher, year, edition, pages
2011. Vol. 40, no 13, 2385-2396 p.
Keyword [en]
Dickey-Fuller test, GARCH(1, 1), MODWT, Wavelet decomposition
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-13666DOI: 10.1080/03610926.2010.481371OAI: oai:DiVA.org:hj-13666DiVA: diva2:359820
Available from: 2010-10-30 Created: 2010-10-30 Last updated: 2012-01-16Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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