A Strategy for Testing the Unit Root in AR(1) Model with Intercept. A Monte Carlo Experiment
AbstractIn this paper we introduce a strategy for testing the unit root hypothesis in a first-order autoregressive process with an unknown intercept where the initial value of the variable is a known constant. In the context of this model the standard Dickey-Fuller test is nonsimilar, the intercept being the nuisance parameter. The testing strategy we propose takes into account this non-similarity. It is an unusual two-sided test of the random walk hypothesis since it involves two distributions where the acceptance region is constructed by taking away equal areas for the lower tail of the Student’s t distribution and the upper tail of the distribution tabulated by Dickey and Fuller under the null hypothesis of unit root. In some cases, this strategy does not allow the taking of a direct decision concerning the existence of a unit root. To deal with these situations we suggest testing for the significance of the intercept, and if doubt continues, we use F1 test proposed by Dickey and Fuller (1981). Finally, in order to demonstrate the relevance of non-similarity, Monte Carlo simulations are used to show that the testing strategy is more powerful at stable alternatives and has less size distortions than the two-sided test considered by Dickey and Fuller.
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Bibliographic InfoPaper provided by Centro de Estudios Andaluces in its series Economic Working Papers at Centro de Estudios Andaluces with number E2004/37.
Length: 37 pages
Date of creation: 2004
Date of revision:
unit root; Dickey-Fuller tests; non-similarity; Monte Carlo simulations; empirical size; nominal size;
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2004-05-09 (All new papers)
- NEP-ECM-2004-05-09 (Econometrics)
- NEP-ETS-2004-05-09 (Econometric Time Series)
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