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.

中文翻译：

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方程组的基于小波的方差比单位根检验

摘要 在本文中，我们建议使用基于最大重叠离散小波变换的谱方差分解方法对方程组进行单位根检验。我们获得了检验统计量的极限分布，并使用蒙特卡罗模拟研究了它的小样本特性。我们发现，对于小长度的多个时间序列，基于小波的方法在存在横截面依赖性的情况下对尺寸失真具有鲁棒性。基于小波的测试也比横截面增强的 Im 等人更强大。单位根检验（Pesaran, MH 2007。“A Simple Panel Unit Root Test in Presence of Cross-section Dependence.” Journal of Applied Econometrics 22 (2): 265–312.) 用于时间序列的 20 到 100 个观测值，使用 5 和 10 方程组。