平滑结构突变下Dicke,y-Fuller检验的大样本行为

The Asymptotic Behavior of the Dickey-Fuller Test under the Smooth Structure Changes

Enders和Lee(2012)提出考虑平滑结构突变的傅里叶函数扩展型Dickey-Fuller单位根检验(FADF)。本文研究了当真实数据生成过程包含平滑结构突变时,标准Dickey-Fuller单位根检验的行为。本文证明:忽略结构突变的OLS回归方程中,检验单位根的t统计量的渐进分布与Dickey-Fuller(1979)一样。因此,当真实数据生成过程含傅里叶型结构突变时忽略该结构突变,或不正确地考虑了加入傅里叶项考虑结构突变,标准DF单位根检验的渐进分布依然是大样本可用的。蒙特卡洛模拟的证据与本文的理论相符。然而,模拟也指出:FADF对含平滑结构突变和瞬时结构突变的时间序列都有理想的小样本性质,而不正确地处理傅里叶项会扭曲DF单位根检验的小样本性质。

Enders and Lee （2012） propose a Fourier function augmented Dickey-Fuller unit root test （FADF） under the smooth breaks. This paper considers the asymptotic behavior of the standard Dickey-Fuller unit root test ~when the real data generating process contains smooth breaks. We show that, in the OLS regression, the t-ratio statistics for testing unit root has the same asymptotic distribution as that of Dickey and Fuller （1979）. It means that the asymptotic validity of the DF test under the null is not affected by no allowance for a break if there is a break or by the allowance for a break if there is no break. The Monte Carlo simulations support our theory. Meanwhile, simulation not only indicates that FADF has good performance for time series with smooth breaks or abrupt breaks in small samples but shows that the incorrect treatment of Fourier terms can deteriorate the finite sample properties of DF test.