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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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Suggested Citation

  • Stock, James H., 1994. "Deciding between I(1) and I(0)," Journal of Econometrics, Elsevier, vol. 63(1), pages 105-131, July.
    • Handle: RePEc:eee:econom:v:63:y:1994:i:1:p:105-131
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    Cited by:

    1. Aparicio, Felipe M. & García, Ana, 2003. "Range unit root tests," DES - Working Papers. Statistics and Econometrics. WS ws031126, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Yamin Ahmad & Adam Check & Ming Chien Lo, 2024. "Unit Roots in Macroeconomic Time Series: A Comparison of Classical, Bayesian and Machine Learning Approaches," Computational Economics, Springer;Society for Computational Economics, vol. 63(6), pages 2139-2173, June.
    3. 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.
    4. 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.
    5. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    6. Mira, Santiago, 1997. "Nonlinear cointegration with mixing errors," DES - Working Papers. Statistics and Econometrics. WS 6204, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Vosseler, Alexander, 2016. "Bayesian model selection for unit root testing with multiple structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 616-630.
    8. Mira, Santiago, 1996. "Nonlinear cointegration and nonlinear error correction," DES - Working Papers. Statistics and Econometrics. WS 4546, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Papailias, Fotis & Fruet Dias, Gustavo, 2015. "Forecasting long memory series subject to structural change: A two-stage approach," International Journal of Forecasting, Elsevier, vol. 31(4), pages 1056-1066.
    10. Mehmet Balcilar, 2007. "Point Optimal Invariant Tests of a Unit Root in Models with Structural Change," Working Papers 15-50, Eastern Mediterranean University, Department of Economics.
    11. 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;The Institute of Statistical Mathematics, vol. 59(3), pages 403-423, September.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 195-213, June.
    17. Ahn & Byung Chul, 1994. "Testing the null of stationarity in the presence of structural breaks for multiple time series," Econometrics 9411001, University Library of Munich, Germany, revised 08 Nov 1994.
    18. Blomqvist, A. G. & Carter, R. A. L., 1997. "Is health care really a luxury?," Journal of Health Economics, Elsevier, vol. 16(2), pages 207-229, April.

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