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A Time Series Paradox: Unit Root Tests Perform Poorly When Data Are Cointegrated

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We show that cointegration among times series paradoxically makes it more likely that a unit test will reject the unit root null hypothesis on the individual series. If one time series is cointegrated with another, then it can be written as the sum of two processes, one with a unit root and one stationary. It follows that the series cannot be represented as a finite-order autoregressive process. Unit root tests use an autoregressive model to account for autocorrelation, so they perform poorly in this setting, even if standard methods are used to choose the number of lags. This finding implies that univariate unit root tests are of questionable use in cointegration analysis.

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  • W. Robert Reed & Aaron Smith, 2016. "A Time Series Paradox: Unit Root Tests Perform Poorly When Data Are Cointegrated," Working Papers in Economics 16/19, University of Canterbury, Department of Economics and Finance.
    • Handle: RePEc:cbt:econwp:16/19
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    File URL: https://repec.canterbury.ac.nz/cbt/econwp/1619.pdf
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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
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    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.
    4. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    5. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
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    More about this item

    Keywords

    Unit root testing; cointegration; Augmented Dickey-Fuller test; Akaike Information Criterion (AIC); Bayesian Information Criterion (BIC); Modified Akaike Information Criterion (MAIC);
    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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