Behaviour of Dickey-Fuller unit-root tests under trend misspecification. (English) Zbl 1062.62187

The authors consider the data generating process for \(T\) observations given by \[ y_{t}=\begin{cases}\alpha+\beta_1t+v_{t}, & t\leq\tau T,\\ \alpha+\beta_1\tau T+\beta_2(t-\tau T)+v_{t}, & t>\tau T, \end{cases} \] where \(v_{t}=\rho v_{t-1}+\eta_{t}\) with \(\eta_{t}\) is an i.i.d. sequence with mean zero. It is shown that the Dickey-Fuller test can display a wide range of different characteristics under both the \(I(1)\) null and \(I(0)\) alternative, dependent on the nature and location of the break of trend. In particular, in the case where the data generating process is \(I(1)\) around a broken trend, the authors find that rejection probabilities of the null hypothesis can be very high. In the case where the data generating process is \(I(0)\) around a broken trend, the null hypothesis may still be rejected very frequently.


62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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