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

Ulrich K. Müller

42 citations0/0 files storedEconometric Theory

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Monetary Policy and Economic Impact Complex Systems and Time Series Analysis Diverse Scientific and Economic Studies

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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References

1992Testing the null hypothesis of stationarity against the alternative of a unit root 1980Brownian Motion 2002Nonparametric tests for unit roots and cointegration 2001Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate 2002Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes 1998New Tools for Understanding Spurious Regressions 1992The relationship between power and level for generic unit root tests in finite samples 2004Size and power of tests of stationarity in highly autocorrelated time series

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2013Summability of stochastic processes—A generalization of integration for non-linear processes 2007Testing Covariance Stationarity 2009A POWERFUL TEST OF THE AUTOREGRESSIVE UNIT ROOT HYPOTHESIS BASED ON A TUNING PARAMETER FREE STATISTIC 2009When is a Time‐Series I(0)?*2010Reducing the size distortion of the KPSS test

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