Abstract
Abstract In this paper, we suggest a unit root test for a system of equations using a spectral variance decomposition method based on the Maximal Overlap Discrete Wavelet Transform. We obtain the limiting distribution of the test statistic and study its small sample properties using Monte Carlo simulations. We find that, for multiple time series of small lengths, the wavelet-based method is robust to size distortions in the presence of cross-sectional dependence. The wavelet-based test is also more powerful than the Cross-sectionally Augmented Im et al. unit root test (Pesaran, M. H. 2007. “A Simple Panel Unit Root Test in the Presence of Cross-section Dependence.” Journal of Applied Econometrics 22 (2): 265–312.) for time series with between 20 and 100 observations, using systems of 5 and 10 equations. We demonstrate the usefulness of the test through an application on evaluating the Purchasing Power Parity theory for the Group of 7 countries and find support for the theory, whereas the test by Pesaran (Pesaran, M. H. 2007. “A Simple Panel Unit Root Test in the Presence of Cross-section Dependence.” Journal of Applied Econometrics 22 (2): 265–312.) finds no such support.
Highlights
Testing for unit roots in systems of equations has been an active area of research for at least the last three decades
The principal aim of this research has been to increase the power of unit root tests by utilizing the cross-sectional dimension of multiple time series
A unit root test for a system of equations is introduced in this paper
Summary
Testing for unit roots in systems of equations has been an active area of research for at least the last three decades. The principal aim of this research has been to increase the power of unit root tests by utilizing the cross-sectional dimension of multiple time series. In this way, power gains can be made by increasing the overall number of observations while using relatively short time series. Im, Pesaran, and Shin (2003) presented the IPS test, which relaxed this assumption and modeled the individual time series using separate linear trends. Their suggested test statistic was the average of the t-statistics from the individual equations. The test has been revealed to be sensitive to cross-sectional dependency (see Li and Shukur, 2013, for example)
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