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Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series

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  • Nunzio Cappuccio

    (Department of Economics and Management “Marco Fanno”, via del Santo 33, Padova 35123, Italy)

  • Diego Lubian

    (Department of Economics, University of Verona, via dell’Artigliere 19, Verona 37129, Italy)

Abstract

In cointegration analysis, it is customary to test the hypothesis of unit roots separately for each single time series. In this note, we point out that this procedure may imply large size distortion of the unit root tests if the DGP is a VAR. It is well-known that univariate models implied by a VAR data generating process necessarily have a finite order MA component. This feature may explain why an MA component has often been found in univariate ARIMA models for economic time series. Thereby, it has important implications for unit root tests in univariate settings given the well-known size distortion of popular unit root test in the presence of a large negative coefficient in the MA component. In a small simulation experiment, considering several popular unit root tests and the ADF sieve bootstrap unit tests, we find that, besides the well known size distortion effect, there can be substantial differences in size distortion according to which univariate time series is tested for the presence of a unit root.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jecnmx:v:4:y:2016:i:2:p:21-:d:67747
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    References listed on IDEAS

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