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The Impossibility Of Consistent Discrimination Between I(0) And I(1) Processes

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  • MÜller, Ulrich K.

Abstract

An I(0) process is commonly defined as a process that satisfies a functional central limit theorem, i.e., whose scaled partial sums converge weakly to a Wiener process, and an I(1) process as a process whose first differences are I(0). This paper establishes that with this definition, it is impossible to consistently discriminate between I(0) and I(1) processes. At the same time, on a more constructive note, there exist consistent unit root tests and also nontrivial inconsistent stationarity tests with correct asymptotic size.

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  • MÜller, Ulrich K., 2008. "The Impossibility Of Consistent Discrimination Between I(0) And I(1) Processes," Econometric Theory, Cambridge University Press, vol. 24(3), pages 616-630, June.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:616-630_08
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    Cited by:

    1. Castro, Tomás del Barrio & Rodrigues, Paulo M.M. & Taylor, A.M. Robert, 2013. "The Impact Of Persistent Cycles On Zero Frequency Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1289-1313, December.
    2. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2013. "On the Testability of Identification in Some Nonparametric Models With Endogeneity," Econometrica, Econometric Society, vol. 81(6), pages 2535-2559, November.
    3. Berenguer Rico, Vanessa, 2011. "Summability of stochastic processes: a generalization of integration and co-integration valid for non-linear processes," UC3M Working papers. Economics we1115, Universidad Carlos III de Madrid. Departamento de Economía.

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