单位根检验中样本长度的选择

Selection of Sample Length in Unit Root Test

单位根检验在实证分析中应用非常广泛,但很多应用只关注检验水平而忽略检验功效的影响,没有注意到样本数过小时根本得不到可靠的检验结果。本文从理论上推导了单位根检验功效的估算公式,研究了检验功效的影响因素,并在此基础上,推导了单位根检验中样本长度最低要求的估算公式。并利用仿真数据,用曲线拟合的方法,推出了实证分析中估算最小样本长度的公式。从而对单位根检验实证分析中的样本选择提供了理论和实际依据;同时表明,因为样本总是有限的,实证分析中是没法判断ρ是否严格为1的,而只能将ρ大于接近于1的某个值时都看作单位根过程,并提供检验功效以供参考。

Unit root test is used widely in empirical analysis, but many applications focus only on test sizes and ignore test powers, leading to suspicious results especially when samples are small. This paper deduces the theoretical formula of test power in unit root test, researches the impacting factors of test power and proposes the estimated formula of the smallest sample length. Based on the simulation data and curve estimation, the fitted formula of the smallest sample length is offered, which addresses theoretical and practical basis of sample choice in empirical analysis of unit root. At the same time, because samples are always finite in empirical analysis, it＇s impossible to judge whether p equals to 1 or not strictly, so we have to take ρ ≥ ρ0 （ρ0 is some value near 1） as unit root process and offer the test power as reference.