中文摘要：

本文引入局部趋势概念,研究数据生成和检验式都含有趋势单位根过程中伪t检验量的分布,结果表明该分布为标准正态分布与第四种DF分布的混合体,并揭示了向这两类分布转化的条件。为摆脱伪t检验量受到特定参数约束而不能用于实证分析的困境,本文提出了Bootstrap检验方法,并从理论上证明该方法可用于水平检验和功效研究,埃奇沃思展开进一步证实该方法能够降低水平扭曲。蒙特卡洛模拟结果显示,Bootstrap检验量具有最高检验正确率,检验功效在一定条件下也能与标准正态分布的检验结果相媲美,说明Bootstrap方法可以用于此类模型的单位根检验。

英文摘要：

This paper first introduces the concept of local trend and analyzes the distribution of pseudo t statistics for the testing model which is the same as the data generating process,that is,produced by unit root process with trend,concluding that this is a mixture of standard normal distribution and the fourth dickey-fuller distribution,and the conditions converting to these two distributions are also proposed. Meanwhile,to avoid the plight that the pseudo t statistics can not be applied to empirical research due to its constraints to specific parameters,we offer the Bootstrap method and testify its validity for size and power research as well as the Edgeworth expansion is used to confirm its superiority to reduce the size distortion. Finally,we conduct the Monte Carlo simulation,and the results show that the accuracy from Bootstrap method is the highest and the testing power is comparable to the critic value method based on standard normal distribution under certain conditions,which means that the Bootstrap method can be used to execute the unit root test for this model. This paper both enriches the theory for unit root test and expands the application fields of Bootstrap method.