The impossibility of consistent discrimination between I(0) and I(1) processes

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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.

Original languageEnglish (US)
Pages (from-to)616-630
Number of pages15
JournalEconometric Theory
Volume24
Issue number3
DOIs
StatePublished - Jun 1 2008

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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