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Deciding Between I(1) and I(0)


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  • James H. Stock


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

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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Publication status: published as Journal of Econometrics, vol. 63 (1994) pp 105-131.
Handle: RePEc:nbr:nberte:0121

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Cited by:
  1. Felipe M. Aparicio & Alvaro Escribano & Ana García, 2004. "A Range Unit Root Test," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws041104, Universidad Carlos III, Departamento de Estadística y Econometría.
  2. 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, Springer, vol. 12(1), pages 195-213, June.
  3. Blomqvist, A.G. & Carter, R.A.L., 1993. "Is Health Care Really a Luxury?," UWO Department of Economics Working Papers, University of Western Ontario, Department of Economics 9311, University of Western Ontario, Department of Economics.
  4. Umino, Shingo, 2014. "Real-time estimation of the equilibrium real interest rate: Evidence from Japan," The North American Journal of Economics and Finance, Elsevier, Elsevier, vol. 28(C), pages 17-32.
  5. Kramer, Walter & Davies, Laurie, 2002. "Testing for unit roots in the context of misspecified logarithmic random walks," Economics Letters, Elsevier, Elsevier, vol. 74(3), pages 313-319, February.
  6. Chen, Pei-Fen & Chien, Mei-Se & Lee, Chien-Chiang, 2011. "Dynamic modeling of regional house price diffusion in Taiwan," Journal of Housing Economics, Elsevier, Elsevier, vol. 20(4), pages 315-332.
  7. Gil-Alana, L. A. & Robinson, P. M., 1997. "Testing of unit root and other nonstationary hypotheses in macroeconomic time series," Journal of Econometrics, Elsevier, Elsevier, vol. 80(2), pages 241-268, October.
  8. Felipe M. Aparicio & Alvaro Escribano & Ana García, 2003. "Range Unit Root Tests," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws031126, Universidad Carlos III, Departamento de Estadística y Econometría.
  9. Nunzio Cappuccio & Diego Lubian, 2003. "Asymptotic null distributions of stationarity and nonstationarity," Working Papers, University of Verona, Department of Economics 8, University of Verona, Department of Economics.
  10. 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, Springer, vol. 59(3), pages 403-423, September.
  11. Pascalau, Razvan, 2008. "Unit Roots Tests with Smooth Breaks: An Application to the Nelson-Plosser Data Set," MPRA Paper 7220, University Library of Munich, Germany.
  12. Ahn & Byung Chul, 1994. "Testing the null of stationarity in the presence of structural breaks for multiple time series," Econometrics, EconWPA 9411001, EconWPA, revised 08 Nov 1994.
  13. Kunst, Robert M., 2005. "Approaches for the Joint Evaluation of Hypothesis Tests: Classical Testing, Bayes Testing, and Joint Confirmation," Economics Series, Institute for Advanced Studies 177, Institute for Advanced Studies.


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