单位根检验中的Wald检验量研究：Bootstrap法VS临界值法

针对Wald临界值检验方法存在检验水平扭曲和功效低下的不足，提出了Wald检验量的Bootstrap检验方法，并从理论上证明了该方法的有效性；借助于蒙特卡罗模拟技术对两种检验方法进行对比.结果表明：在无漂移项数据生成过程中，两种方法的实际覆盖率分别为100%和72.9%，精确程度之比为33：15；在有漂移项的数据生成过程中，实际覆盖率分别为94.4%和77.8%，精确程度之比为20：15；在检验功效方面，Bootstrap方法较临界值检验具有明显的优势，尤其是在小样本下；由标准正态分布得到的临界值对其它误差分布类型缺乏稳健性.实证分析也表明由Bootstrap检验方法得到的模型更符合实际情况.因此，Bootstrap方法可以替代临界值方法进行单位根的Wald检验.

Research on unit root test in Wald statistics: Bootstrap VS critic value method

The Bootstrap method for Wald statistics is proposed for the drawbacks of the critic value method due to its size distortion and lower power, and the validity is also testified. With the use of Monte Carlo simulation, the results between the Bootstrap method and the critic value method are compared. When the data is generated without drift term, the outcomes from simulation show that the coverage rates are 100% and 72.9% for Bootstrap method and critic value method respectively, while the ratio for precision is 33 to 15. But when drift term is combined, the coverage rate is 94.4% and 77.8% for each method, and the ratio for precision is 20 to 15. With referenced to test power, the Bootstrap method has an obvious advantage over critic value method, especially in small sample size. The critic values from standard normal distribution are lack of robustness for other types of error distribution. The empirical analysis shows that the models constructed from Bootstrap test method are more in line with the actual situations. All these results suggest that the Bootstrap method can replace the critic value method to perform unit root test with Wald statistics.