Power of Unit Root Tests Against Nonlinear and Noncausal Alternatives with an Application to the Brent Crude Oil Price

Bec Frédérique (), Guay Alain (), Nielsen Heino Bohn () and Saïdi Sarra ()
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Bec Frédérique: Thema, CY Cergy Paris University, Cergy and CREST, Palaiseau, France
Guay Alain: Université du Québec à Montréal, Montreal, Canada
Nielsen Heino Bohn: Department of Economics, University of Copenhagen, Copenhagen, Denmark
Saïdi Sarra: Thema, CY Cergy Paris University, Cergy, France

Studies in Nonlinear Dynamics & Econometrics, 2025, vol. 29, issue 1, 1-18

Abstract: The increasing sophistication of economic and financial time series modelling creates a need for a test of the time dependence structure of the series which does not require a proper specification of the alternative. Indeed, the latter is unknown beforehand. Yet, the stationarity has to be established before proceeding to the estimation and testing of causal/noncausal or linear/nonlinear models as their econometric theory has been developed under the maintained assumption of stationarity. In this paper, we propose a new unit root test statistics which is both asymptotically consistent against all stationary alternatives and still keeps good power properties in finite sample. A large simulation study is performed to assess the power of our test compared to existing unit root tests built specifically for various kinds of stationary alternatives, when the true DGP is either causal or noncausal, linear or nonlinear stationary. Based on various sample sizes and degrees of persistence, it turns out that our new test performs very well in terms of power in finite sample, no matter the alternative under consideration. The proposed approach is illustrated using recent Brent crude oil price data.

Keywords: unit root test; threshold autoregressive model; noncausal model; oil price (search for similar items in EconPapers)
JEL-codes: C12 C22 C46 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/snde-2022-0084

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