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Limit Theory for VARs with Mixed Roots Near Unity

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  • Peter C. B. Phillips
  • Ji Hyung Lee

Abstract

Limit theory is developed for nonstationary vector autoregression (VAR) with mixed roots in the vicinity of unity involving persistent and explosive components. Statistical tests for common roots are examined and model selection approaches for discriminating roots are explored. The results are useful in empirical testing for multiple manifestations of nonstationarity - in particular for distinguishing mildly explosive roots from roots that are local to unity and for testing commonality in persistence.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:1035-1056
    DOI: 10.1080/07474938.2014.956617
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    References listed on IDEAS

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    1. Peter C.B. Phillips, 2008. "Unit Root Model Selection," Cowles Foundation Discussion Papers 1653, Cowles Foundation for Research in Economics, Yale University.
    2. 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.
    3. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    4. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    5. Werner Ploberger & Peter C. B. Phillips, 2003. "Empirical Limits for Time Series Econometric Models," Econometrica, Econometric Society, vol. 71(2), pages 627-673, March.
    6. Xu Cheng & P eter C. B. Phillips, 2009. "Semiparametric cointegrating rank selection," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 83-104, January.
    7. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
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    Citations

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    Cited by:

    1. Yubo Tao & Jun Yu, 2020. "Model Selection for Explosive Models," Advances in Econometrics, in: Essays in Honor of Cheng Hsiao, volume 41, pages 73-103, Emerald Group Publishing Limited.
    2. Phillips, Peter C.B. & Lee, Ji Hyung, 2016. "Robust econometric inference with mixed integrated and mildly explosive regressors," Journal of Econometrics, Elsevier, vol. 192(2), pages 433-450.
    3. Stauskas, Ovidijus, 2019. "On the Limit Theory of Mixed to Unity VARs: Panel Setting With Weakly Dependent Errors," Working Papers 2019:2, Lund University, Department of Economics.
    4. Marie Badreau & Frédéric Proïa, 2023. "Consistency and asymptotic normality in a class of nearly unstable processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 619-641, October.
    5. Ye Chen & Jian Li & Qiyuan Li, 2023. "Seemingly Unrelated Regression Estimation for VAR Models with Explosive Roots," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(4), pages 910-937, August.
    6. Ovidijus Stauskas, 2020. "On the limit theory of mixed to unity VARs: Panel setting with weakly dependent errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(6), pages 892-898, November.

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