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Univariate Unit Root Tests Perform Poorly When Data Are Cointegrated

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Abstract

This note 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 in reasonably sized samples. While the addition of lagged differenced (LD) terms can sometimes eliminate the size distortion, standard diagnostics such as (i) testing for serial correlation in the residuals and (ii) using information criteria to select lags are unable to identify the appropriate number of terms.

Suggested Citation

  • W. Robert Reed, 2016. "Univariate Unit Root Tests Perform Poorly When Data Are Cointegrated," Working Papers in Economics 16/01, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:16/01
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    File URL: https://repec.canterbury.ac.nz/cbt/econwp/1601.pdf
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    References listed on IDEAS

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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. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    3. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
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    1. repec:arp:tjssrr:2019:p:876-887 is not listed on IDEAS
    2. 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.

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    More about this item

    Keywords

    Unit root testing; cointegration; DF-GLS test; Augmented Dickey-Fuller test; Phillips-Perron test; Monte Carlo; 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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