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A Comparison of Alternative Unit Root Tests

机译：替代单位根检验的比较

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摘要

In this paper we evaluate the performance of three methods for testing the existence of a unit root in a time series, when the models under consideration in the null hypothesis do not display autocorrelation in the error term. In such cases, simple versions of the Dickey-Fuller test should be used as the most appropriate ones instead of the known augmented Dickey-Fuller or Phillips-Perron tests. Through Monte Carlo simulations we show that, apart from a few cases, testing the existence of a unit root we obtain actual type I error and power very close to their nominal levels. Additionally, when the random walk null hypothesis is true, by gradually increasing the sample size, we observe that p-values for the drift in the unrestricted model fluctuate at low levels with small variance and the Durbin-Watson (DW) statistic is approaching 2 in both the unrestricted and restricted models. If, however, the null hypothesis of a random walk is false, taking a larger sample, the DW statistic in the restricted model starts to deviate from 2 while in the unrestricted model it continues to approach 2. It is also shown that the probability not to reject that the errors are uncorrelated, when they are indeed not correlated, is higher when the DW test is applied at 1% nominal level of significance.
机译：当无效假设中考虑的模型在误差项中不显示自相关时，本文评估了三种测试时间序列中单位根存在的方法的性能。在这种情况下，应使用简单版本的Dickey-Fuller测试代替已知的增强Dickey-Fuller或Phillips-Perron测试。通过蒙特卡洛模拟，我们表明，除少数情况外，测试单位根的存在，我们会获得实际的I型误差和功率，非常接近其标称水平。此外，当随机游走原假设为真时，通过逐渐增加样本数量，我们观察到无限制模型中的漂移的p值在较低水平波动且方差很小，并且Durbin-Watson（DW）统计值接近2在不受限制和受限制的模型中。但是，如果随机游走的零假设为假，则采用更大的样本，则受限模型中的DW统计量开始偏离2，而非受限模型中的DW统计量继续接近2。这也表明概率不当以1％的名义显着性水平应用DW测试时，拒绝错误是不相关的（当确实不相关时）会更高。

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