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Deciding between I(1) and I(0)

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  • Stock, James H.

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 63 (1994)
Issue (Month): 1 (July)
Pages: 105-131

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Handle: RePEc:eee:econom:v:63:y:1994:i:1:p:105-131

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Web page: http://www.elsevier.com/locate/jeconom

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Cited by:
  1. Kramer, Walter & Davies, Laurie, 2002. "Testing for unit roots in the context of misspecified logarithmic random walks," Economics Letters, Elsevier, vol. 74(3), pages 313-319, February.
  2. Blomqvist, A.G. & Carter, R.A.L., 1993. "Is Health Care Really a Luxury?," UWO Department of Economics Working Papers 9311, University of Western Ontario, Department of Economics.
  3. 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.
  4. María Presno & Anna López, 2003. "Testing for stationarity in series with a shift in the mean. A fredholm approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 12(1), pages 195-213, June.
  5. Nunzio Cappuccio & Diego Lubian, 2007. "Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(3), pages 403-423, September.
  6. Razvan Pascalau, 2010. "Unit root tests with smooth breaks: an application to the Nelson-Plosser data set," Applied Economics Letters, Taylor & Francis Journals, vol. 17(6), pages 565-570.
  7. Kunst, Robert M., 2005. "Approaches for the Joint Evaluation of Hypothesis Tests: Classical Testing, Bayes Testing, and Joint Confirmation," Economics Series 177, Institute for Advanced Studies.
  8. Nunzio Cappuccio & Diego Lubian, 2003. "Asymptotic null distributions of stationarity and nonstationarity," Working Papers 8, University of Verona, Department of Economics.
  9. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, vol. 80(2), pages 241-268, October.
  10. 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.
  11. 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.
  12. Umino, Shingo, 2014. "Real-time estimation of the equilibrium real interest rate: Evidence from Japan," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 17-32.
  13. Chen, Pei-Fen & Chien, Mei-Se & Lee, Chien-Chiang, 2011. "Dynamic modeling of regional house price diffusion in Taiwan," Journal of Housing Economics, Elsevier, vol. 20(4), pages 315-332.

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