永久性结构变化下Dickey-Fuller检验的伪拒绝研究

Spurious rejections of Dickey-Fuller tests under permanent breaks

使用傅里叶变换处理结构突变是单位根检验中的流行方法之一,其中整数频率和分数频率分别对应暂时性结构变化和永久性结构变化,这一区分在实证应用中具有重要的经济含义,但其对计量理论的影响尚不清楚.本文研究当真实数据生成过程包含分数频率傅里叶型结构变化时,忽略傅里叶项对标准Dickey-Fuller单位根检验性质的影响.通过重新参数化,推导了相应的极限分布,探讨极限结果对标准Dickey-Fuller检验性质的理论预测,给出了Dickey-Fuller检验伪拒绝发生的条件.模拟的证据与本文的理论结果一致.研究结果表明:永久性结构变化更容易引起Dickey-Fuller检验的伪拒绝问题.因此,忽略分数频率傅里叶项或将其误设为整数频率都会导致错误的实证结果.

It is a popular method to deal with structural breaks using Fourier transformation,in which an integer frequency and a fractional frequency are respectively associated with transitory and permanent breaks,and hence is important in empirical applications.However,we still do not know how the integer and fractional frequencies affect the theoretical properties of unit root tests.This paper examines the properties of Dickey-Fuller tests when the true datagenerating process contains fractional Fourier-form breaks but ignored in testing procedures.We derive the limiting distributions by reparameterization,discuss the theoretical predictions of the limiting results on the properties of Dickey-Fuller tests,and give the conditions under which spurious rejection occurs.We use Monte Carlos simulations to confirm the predictions,finding that the theory is consistent with the simulation evidence.Our results imply that permanent breaks could more easily lead to spurious rejections than temporary breaks.Thus,ignoring a fractional frequency or specifying it as integer would cause misleading results.