DF检验式中漂移项和趋势项的t统计量研究

Distribution of the t-Statistics of the Drift and the Time Trend for Unit Root Test

DF统计量的渐近分布决定于估计的回归中,是否包含一个常数项α或时间趋势δ以及真实随机行走是否有非零漂移项表征,故通常的DF检验过程中包含三种检验式(不含α和δ、只含α、含α和δ)。针对α和δ及其t统计量的分布特征的研究甚少,对它们的极限分布未见有全面的推导,且关于单个回归参数检验统计量的响应面函数目前还无人提供。本文的贡献在于推导了不同检验式中α和δ的t检验统计量的极限分布表达式,并通过蒙特卡罗模拟结果分析了α和δ及其t统计量的分布特征,在此基础上给出有限样本下各检验统计量的响应面函数,从而使得DF检验进一步完善。

The asymptotic distributions of certain statistics involving unit root processes such as Dickey-Fuller statistics depend on whether a constant or time trend is included in the estimated regression and the true random walk is characterized by nonzero drift. Generally, the dickey-fuller tests include three test equations （with intercept α and trend δ, only intercept α, none） . The distribution properties of the intercept or the time trend and that of its t-statistics are seldom dis cussed. As far as we know, there are no whole and explicit processes deducing the limit distributions. This paper will derive these distributions; analyse the properties of the small sample distributions and present the response surface functions for various finite sample sizes using Monte Carlo simulations. It helps to make DF test perfect further. It makes DF test result impeccable as well.