Scandinavian Working Papers in Economics

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

No 2009:7: Wavelet Improvement of the Over-rejection of Unit root test under GARCH errors

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 use the wavelet technique to improve the over-rejection problem of the traditional Dickey-Fuller test for unit root when the data suffers from GARCH (1,1) effect. The logic is based on that the wavelet spectrum decomposition can separate out information of different frequencies in the data series. We prove that the asymptotic distribution of our test is similar to the traditional Dickey-Fuller(1979 and 1981) type of tests. The small sample distribution of the new test is assessed by means of Monte Carlo simulation. An empirical example with data on immigration to Sweden during the period 1950 to 2000 is used to illustrate the test. The results reveal that using the traditional Dickey-Fuller type of test, the unit root is rejected while our wavelet improved test shows the opposite result.

Keywords: Dickey-Fuller test; GARCH (1:1); Wavelet spectrum decomposition; MODWT

JEL-codes: C15; C52

9 pages, February 26, 2009

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