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THE IMPOSSIBILITY OF CONSISTENT DISCRIMINATION BETWEEN I(0) AND I(1) PROCESSES

Published online by Cambridge University Press:  22 January 2008

Ulrich K. MÜller
Ulrich K. MÜller
Affiliation:
Princeton University
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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.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 3 , June 2008 , pp. 616 - 630
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Blough, S.R. (1992) The relationship between power and level for generic unit root tests in finite samples. Journal of Applied Econometrics 7, 295–308.CrossRefGoogle Scholar
Breitung, J. (2002) Nonparametric tests for unit roots and cointegration. Journal of Econometrics 108, 343–363.CrossRefGoogle Scholar
Caner, M. ’ Kilian, L. (2001) Size distortions of tests of the null hypothesis of stationarity: Evidence and implications for the PPP debate. Journal of International Money and Finance 20, 639–657.CrossRefGoogle Scholar
Corradi, V. (1999) Deciding between I(0) and I(1) via FLIL-based bounds. Econometric Theory 14, 643–663.CrossRefGoogle Scholar
Davidson, J. (1999) When Is a Time Series I(0)? Evaluating the Memory Properties of Nonlinear Dynamic Models. Mimeo, Cardiff University.Google Scholar
Davidson, J. (2002) Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes. Journal of Econometrics 106, 243–269.CrossRefGoogle Scholar
Faust, J. (1996) Near observational equivalence and theoretical size problems with unit root tests. Econometric Theory 12, 724–731.CrossRefGoogle Scholar
Hida, T. (1980) Brownian Motion. Springer-Verlag.CrossRefGoogle Scholar
Itô, K. ’ Nisio, M. (1968) On the convergence of sums of independent Banach space valued random variables. Osaka Journal of Mathematics 5, 35–48.Google Scholar
Kiefer, N.M. ’ Vogelsang, T.J. (2005) A new asymptotic theory for heteroskedasticity-autocorrelation robust tests. Econometric Theory 21, 1130–1164.CrossRefGoogle Scholar
Kiefer, N.M., Vogelsang, T.J., ’ Bunzel, H. (2000) Simple robust testing of regression hypotheses. Econometrica 68, 695–714.CrossRefGoogle Scholar
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., ’ Shin, Y. (1992) Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54, 159–178.CrossRefGoogle Scholar
Müller, U.K. (2005) Size and power of tests of stationarity in highly autocorrelated time series. Journal of Econometrics 128, 195–213.CrossRefGoogle Scholar
Müller, U.K. (2007) A theory of robust long-run variance estimation. Journal of Econometrics 141, 1331–1352.CrossRefGoogle Scholar
Phillips, P.C.B. (1998) New tools for understanding spurious regression. Econometrica 66, 1299–1325.CrossRefGoogle Scholar
Phillips, P.C.B. ’ Ploberger, W. (1996) An asymptotic theory of Bayesian inference for time series. Econometrica 64, 381–412.CrossRefGoogle Scholar
Pollard, D. (2002) A User's Guide to Measure Theoretic Probability. Cambridge University Press.Google Scholar
Pötscher, B.M. (2002) Lower risk bounds and properties of confidence sets for ill-posed estimation problems with applications to spectral density and persistence estimation, unit roots, and estimation of long memory parameters. Econometrica 70, 1035–1065.CrossRefGoogle Scholar
Stock, J.H. (1994) Deciding between I(1) and I(0). Journal of Econometrics 63, 105–131.CrossRefGoogle Scholar
White, H. (2001) Asymptotic Theory for Econometricians, rev. ed.Academic Press.Google Scholar