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Testing for unit roots with cointegrated data

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  • Reed, W. Robert

Abstract

This paper demonstrates that unit root tests can suffer from inflated Type I error rates when data are cointegrated. Results from Monte Carlo simulations show that three commonly used unit root tests - the ADF, Phillips-Perron, and DF-GLS tests - frequently overreject the true null of a unit root for at least one of the cointegrated variables. The reason for this overrejection is that unit root tests, designed for random walk data, are often misspecified when data are cointegrated. While the addition of lagged differenced (LD) terms can eliminate the size distortion, this "success" is spurious, driven by collinearity between the lagged dependent variable and the LD explanatory variables. Accordingly, standard diagnostics such as (i) testing for serial correlation in the residuals and (ii) using information criteria to select among different lag specifications are futile. The implication of these results is that researchers should be conservative in the weight they attach to individual unit root tests when determining whether data are cointegrated.

Suggested Citation

  • Reed, W. Robert, 2015. "Testing for unit roots with cointegrated data," Economics Discussion Papers 2015-57, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwedp:201557
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    References listed on IDEAS

    as
    1. Harris, R. I. D., 1992. "Testing for unit roots using the augmented Dickey-Fuller test : Some issues relating to the size, power and the lag structure of the test," Economics Letters, Elsevier, vol. 38(4), pages 381-386, April.
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    More about this item

    Keywords

    unit root testing; cointegration; DF-GLS test; augmented Dickey-Fuller test; Phillips-Perron test; simulation;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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