This paper derives asymptotic theory for Breitung's (2002, Journal of Econometrics 108, 343-363) nonparameteric variance ratio unit root test when applied to regression residuals. The test requires neither the specification of the correlation structure in the data nor the choice of tuning parameters. Compared with popular residuals-based no-cointegration tests, the variance ratio test is less prone to size distortions but has smaller local asymptotic power. However, this paper shows that local asymptotic power properties do not serve as a useful indicator for the power of residuals-based no-cointegration tests in finite samples. In terms of size-corrected power, the variance ratio test performs relatively well and, in particular, does not suffer from power reversal problems detected for, e.g., the frequently used augmented Dickey-Fuller type no-cointegration test. An application to daily prices of cryptocurrencies illustrates the usefulness of the variance ratio test in practice.

翻译：本文为Breitung的“非参数差异单位根基测试”(2002年,《经济学期刊》108,343-363)中的非参数性理论,适用于回归残留物时的非参数差异单位根基测试。测试既不要求说明数据中的相关结构,也不要求选择调试参数。与流行的基于残留物的不相容测试相比,差异比率测试不易发生体积扭曲,但具有较小的当地无症状力量。然而,本文显示,本地的无症状功率特性不能作为基于残留物的不相容测试在有限样本中的力量的有用指标。在大小校正功率方面,差异比率测试效果相对较好,特别是没有遇到所检测到的功率逆转问题,例如,经常使用的增强的Dickey-Fuller型不相连接测试。对日均价的隐性调节力应用说明了差异比率测试在实践中的效用。