关键词: 傅里叶函数扩展型单位根检验(FADF), 标准DF检验, 检验功效

Abstract: 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 -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.

Key words: Fourier function augmented DF unit root test, Standard DF Test, Power