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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

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Volume 24 (2020)

A wavelet-based variance ratio unit root test for a system of equations

Abdul Aziz Ali / Kristofer Månsson / Ghazi Shukur
Published Online: 2019-11-16 | DOI: https://doi.org/10.1515/snde-2018-0005


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.

Keywords: system of equations; unit roots; wavelets


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About the article

Published Online: 2019-11-16

Citation Information: Studies in Nonlinear Dynamics & Econometrics, 20180005, ISSN (Online) 1558-3708, DOI: https://doi.org/10.1515/snde-2018-0005.

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