A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
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For testing unit root in single time series, most tests concentrate on the time domain. Recently, Fan and Gençay (Econom Theory 26:1305---1331, 2010) proposed a wavelet ratio test which took advantage of the information from the frequency domain by using a wavelet spectrum methodology. This test shows a better power than many time domain based unit root tests including the Dickey---Fuller (J Am Stat Assoc 74:427---431, 1979) type of test in the univariate time series case. On the other hand, various unit root tests in multivariate time series have appeared since the pioneering work of Levin and Lin (Unit root test in panel data: new results, University of California at San Diego, Discussion Paper, 1993). Among them, the Im---Pesaran---Shin (IPS) (J Econ 115(1):53---74, 1997) test is widely used for its straightforward implementation and robustness to heterogeneity. The IPS test is a group mean test which uses the average of the test statistics for each single series. As the test statistics in each series can be flexible, this paper will apply the wavelet ratio statistic to give a comparison with the test by using Dickey---Fuller t statistic in the single series. Simulation results show a gain in power by employing the wavelet ratio test instead of the Dickey---Fuller t statistic in the panel data case. As the IPS test is sensitive to cross sectional dependence, we further compare the robustness of both test statistics when there exists cross correctional dependence among the units in the panel data. Finally we apply a residual based wavestrapping methodology to reduce the over biased size problem brought up by the cross correlation for both test statistics.