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Unit Root Tests, Size Distortions, and Cointegrated Data

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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 findings extend previous research which reports size distortions for unit roots tests when the associated error terms are serially correlated (Schwert, 1989; DeJong et al., 1992; Harris, 1992). While the addition to the Dickey-Fuller-type specification of the correct number of lagged differenced (LD) terms can eliminate the size distortion, I demonstrate that determining the correct number of LD terms is unachievable in practice. Standard diagnostics such as testing for serial correlation in the residuals, and using information criteria to compare different lag specifications, are unable to identify the requird number of lags. A unique feature of this study is that it includes programs (an Excel spreadsheet and Stata .do files) that allow the reader to simulate their own cointegrated data -- using parameters of their own choosing -- to confirm the findings reported in this paper.

Suggested Citation

  • W. Robert Reed, 2014. "Unit Root Tests, Size Distortions, and Cointegrated Data," Working Papers in Economics 14/28, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:14/28
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    File URL: https://repec.canterbury.ac.nz/cbt/econwp/1428.pdf
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    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.
    2. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
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    Cited by:

    1. Nunzio Cappuccio & Diego Lubian, 2016. "Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series," Econometrics, MDPI, vol. 4(2), pages 1-11, April.
    2. Ingrid Groessl & Artur Tarassow, 2015. "A Microfounded Model of Money Demand Under Uncertainty, and some Empirical Evidence," Macroeconomics and Finance Series 201504, University of Hamburg, Department of Socioeconomics, revised Jan 2018.

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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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