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Unit Root Model Selection

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Abstract

Some limit properties for information based model selection criteria are given in the context of unit root evaluation and various assumptions about initial conditions. Allowing for a nonparametric short memory component, standard information criteria are shown to be weakly consistent for a unit root provided the penalty coefficient C_n -> infinity and C_n/n -> 0 as n -> infinity. Strong consistency holds when C_n/(loglog n)^3 -> infinity under conventional assumptions on initial conditions and under a slightly stronger condition when initial conditions are infinitely distant in the unit root model. The limit distribution of the AIC criterion is obtained.

Suggested Citation

  • Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1653
    Note: CFP 1231.
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d16/d1653.pdf
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    References listed on IDEAS

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    1. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    2. Lai, T. L. & Wei, C. Z., 1982. "Asymptotic properties of projections with applications to stochastic regression problems," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 346-370, September.
    3. Bent Nielsen, 2001. "Order determination in general vector autoregressions," Economics Papers 2001-W10, Economics Group, Nuffield College, University of Oxford.
    4. Hirotugu Akaike, 1969. "Fitting autoregressive models for prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 243-247, December.
    5. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    6. Jae-Young Kim, 1998. "Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models," Econometrica, Econometric Society, vol. 66(2), pages 359-380, March.
    7. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
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    Cited by:

    1. Cheng, Xu & Phillips, Peter C.B., 2012. "Cointegrating rank selection in models with time-varying variance," Journal of Econometrics, Elsevier, vol. 169(2), pages 155-165.
    2. Fabozzi, Frank J. & Xiao, Keli, 2017. "Explosive rents: The real estate market dynamics in exuberance," The Quarterly Review of Economics and Finance, Elsevier, vol. 66(C), pages 100-107.
    3. Peter C. B. Phillips & Ji Hyung Lee, 2015. "Limit Theory for VARs with Mixed Roots Near Unity," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 1035-1056, December.
    4. Xu Cheng & P eter C. B. Phillips, 2009. "Semiparametric cointegrating rank selection," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 83-104, January.
    5. Peter C.B. Phillips & Ji Hyung Lee, 2012. "VARs with Mixed Roots Near Unity," Cowles Foundation Discussion Papers 1845, Cowles Foundation for Research in Economics, Yale University.
    6. Ronald W. Butler & Marc S. Paolella, 2017. "Autoregressive Lag—Order Selection Using Conditional Saddlepoint Approximations," Econometrics, MDPI, vol. 5(3), pages 1-33, September.
    7. Lingjie Du & Tianxiao Pang, 2021. "Asymptotic Theory for a Stochastic Unit Root Model with Intercept and Under Mis-Specification of Intercept," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 767-799, September.
    8. Peter C. B. Phillips & Jun Yu, 2011. "Dating the timeline of financial bubbles during the subprime crisis," Quantitative Economics, Econometric Society, vol. 2(3), pages 455-491, November.

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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