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About Trend, the Shift and the Initial Value in Testing of the Hypothesis of a Unit Root
[О Тренде, Сдвиге И Начальном Значении В Тестировании Гипотезы О Наличии Единичного Корня]

Author

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  • Skrobotov, Anton (Скроботов, Антон)

    (Russian Presidential Academy of National Economy and Public Administration (RANEPA))

Abstract

Recent approaches to testing the hypothesis of a unit root that take into account the effect of the initial value, trend and changes in the data using pre-tested of the initial value, trend and shifts, and on the basis of this use the strategy of combining of rejections of several tests. This allows the use of more powerful tests if there is some uncertainty about the model parameters. In this paper we propose a generalization of the approach Harvey et al. (2012b) in the event of uncertainty about the initial value. It is shown that this approach has a low power at high initial value, because it includes tests based on the GLS-detrending. Therefore, we investigate the effectiveness of some tests for unit root ADF-type taking into account the shift at different values of the initial value, and proposes a decision rule based on the additional pre-testing the value of the initial value and the simultaneous use of tests based on the GLS, and OLS-detrending. In addition, modification of the proposed algorithm are discussed: the use of coefficient pre-test of the trend, the possible presence of multiple structural breaks in the trend and the presence of partial information about the location of the shift. The asymptotic behavior of all the tests is analyzed with local representation and autoregressive parameter and parameters in trend and shifts. The proposed modification are showing good properties asymptotically and in finite samples at different values of interfering parameters.

Suggested Citation

  • Skrobotov, Anton (Скроботов, Антон), 2015. "About Trend, the Shift and the Initial Value in Testing of the Hypothesis of a Unit Root [О Тренде, Сдвиге И Начальном Значении В Тестировании Гипотезы О Наличии Единичного Корня]," Published Papers mak6, Russian Presidential Academy of National Economy and Public Administration.
    • Handle: RePEc:rnp:ppaper:mak6
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    References listed on IDEAS

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    More about this item

    Keywords

    Dickey-Fuller test; the local trend; local shift in the trend; the asymptotic local power; uniting of the rejections; pre-testing; several changes in the trend;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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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