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

W. Reed () and Aaron Smith

Working Papers in Economics from University of Canterbury, Department of Economics and Finance

Abstract: 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.

Keywords: Unit root testing; cointegration; Augmented Dickey-Fuller test; Akaike Information Criterion (AIC); Bayesian Information Criterion (BIC); Modified Akaike Information Criterion (MAIC) (search for similar items in EconPapers)
JEL-codes: C18 C22 C32 (search for similar items in EconPapers)
Pages: 14 pages
Date: 2016-09-06
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-sog
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: A time series paradox: Unit root tests perform poorly when data are cointegrated (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:cbt:econwp:16/19

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