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Properties of the ADF Unit Root Test for Models with Trends and Cycles

Author

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  • Barthelemy, F.
  • Lubrano, M.

Abstract

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.

Suggested Citation

  • Barthelemy, F. & Lubrano, M., 1996. "Properties of the ADF Unit Root Test for Models with Trends and Cycles," G.R.E.Q.A.M. 96a13, Universite Aix-Marseille III.
    • Handle: RePEc:fth:aixmeq:96a13
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    Cited by:

    1. Galbraith, JohnW. & Zinde-Walsh, Victoria, 1999. "On the distributions of Augmented Dickey-Fuller statistics in processes with moving average components," Journal of Econometrics, Elsevier, vol. 93(1), pages 25-47, November.

    More about this item

    Keywords

    TIME SERIES; MODELS; ECONOMETRICS;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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