A unit root test is usually carried out by using the regression test introduced by Dickey and Fuller (1979). Under the null hypothesis the series should be a random walk. But a non-stationary series can usually be decomposed into a random walk and a stationary component. This is what is done in additive decompositions between a trend and a cycle. The model considered here lies in the class of UC model developed by Harvey (1989) whose reduced form is an ARIMA (0,1,q) model. In this context, testing for a unit root can be compared to testing for a unit root in an ARIMA constrained model with a moving average polynomial. The paper analyzes the asymptotic distribution of the Dickey and Fuller (DF) test and of the Augmented Dickey and Fuller (ADF) test under this kind of null hypothesis.
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Paper provided by Universite Aix-Marseille III in its series G.R.E.Q.A.M. with number
96a13.
Length: 24 pages Date of creation: 1996 Date of revision: Handle: RePEc:fth:aixmeq:96a13
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Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models