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Econometrics 2016, 4(2), 21; doi:10.3390/econometrics4020021

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

1
Department of Economics and Management “Marco Fanno”, via del Santo 33, Padova 35123, Italy
2
Department of Economics, University of Verona, via dell’Artigliere 19, Verona 37129, Italy
*
Author to whom correspondence should be addressed.
Academic Editor: Kerry Patterson
Received: 17 September 2015 / Revised: 11 March 2016 / Accepted: 16 March 2016 / Published: 7 April 2016
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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. View Full-Text
Keywords: unit root tests; multivariate time series; cointegration unit root tests; multivariate time series; cointegration
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Cappuccio, N.; Lubian, D. Unit Root Tests: The Role of the Univariate Models Implied by Multivariate Time Series. Econometrics 2016, 4, 21.

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