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Deciding Between I(1) and I(0)

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James H. Stock

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Abstract

This paper proposes a class of procedures that consistently classify the stochastic component of a time series as being integrated either of order zero (l(0» or one (l(1» for general 1(0) and 1(1) processes. These procedures entail the evaluation of the asymptotic likelihoods of certain statistics under the 1(0)and 1(1) hypotheses. These likelihoods do not depend on nuisance parameters describing short-run dynamics and diverge asymptotically, so their ratio provides a consistent basis for classifying a process as 1(1) or 1(0). Bayesian inference can be performed by placing prior mass only on the point hypotheses "1(0)" and "1(1)" without needing to specify parametric priors within the classes of 1(0) and 1(1) processes; the result is posterior odds ratios for the 1(0) and 1(1) hypotheses. These procedures are developed for general polynomial and piecewise linear detrending. When applied to the Nelson-Plosser data with linear detrending, they largely support the original Nelson-Plosser inferences. With piecewise-linear detrending these data are typically uninformative, producing Bayes factors that are close to one.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0121.

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Date of creation: Jun 1992
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Handle: RePEc:nbr:nberte:0121

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  1. Felipe M. Aparicio & Alvaro Escribano & Ana García, 2004. "A Range Unit Root Test," Statistics and Econometrics Working Papers ws041104, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  2. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2004. "Nelson And Plosser Revisited: Evidence From Fractional Arima Models," Economics and Finance Discussion Papers 04-16, Economics and Finance Section, School of Social Sciences, Brunel University. [Downloadable!]
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  3. Nunzio Cappuccio & Diego Lubian, 2003. "Asymptotic null distributions of stationarity and nonstationarity," Working Papers 8, Università di Verona, Dipartimento di Scienze economiche. [Downloadable!]
  4. Felipe M. Aparicio & Alvaro Escribano & Ana García, 2003. "Range Unit Root Tests," Statistics and Econometrics Working Papers ws031126, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  5. Ahn & Byung Chul, 1994. "Testing the null of stationarity in the presence of structural breaks for multiple time series," Econometrics 9411001, EconWPA, revised 08 Nov 1994. [Downloadable!]
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