傅里叶型平滑结构突变下Dickey-Fuller检验的功效——兼论Shibor的平稳性

The Power of Dickey-Fuller Test and the Stationarity of Shibor under the Fourier-form Smooth Breaks

通过推导Dickey-Fuller检验功效函数,研究表明:即使中小型的傅里叶型结构突变,都会严重影响Dickey-Fuller检验的功效,从而使得含傅里叶型平滑结构突变的平稳过程被误判为单位根过程。使用3、6、9个月期和一年期Shibor日度数据发现:传统的ADF、PP、DF-GLS和KPSS几乎都指出Shibor是单位根过程;考虑平滑结构突变的单位根检验则在1%的显著性水平下拒绝了单位根的原假设,这表明Shibor是含结构突变的平稳过程。因此,预测Shibor和理解其动态行为必须考虑其结构突变特征。

By deriving the power function of Dickey-Fuller test, we show that even a small or medium break can dramatically deteriorate the power of DF test, hence lead to the conclusion that a stationary process with a smooth break is mistaken as a unit root process. Based on the daily data of Shibor with the periods of 3, 6, 9 and 12 months, the empirical results show that the traditional tests such as ADF, PP, DF-GLS and KPSS all tend to indicate the nonstationarity of Shibor, but the Fourier-augmented Dickey- Fuller test can reject the unit root null at the 1% significant level. This shows that Shibor is stationary with breaks. Therefore, it is necessary to concern the structural breaks in forecasting and understanding the dynamics of Shibor.