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Inconsistent Var Regression With Common Explosive Roots

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  • Phillips, Peter C.B.
  • Magdalinos, Tassos

Abstract

Nielsen (Working paper, University of Oxford, 2009) shows that vector autoregression is inconsistent when there are common explosive roots with geometric multiplicity greater than unity. This paper discusses that result, provides a coexplosive system extension and an illustrative example that helps to explain the finding, gives a consistent instrumental variable procedure, and reports some simulations. Some exact limit distribution theory is derived and a useful new reverse martingale central limit theorem is proved.

Suggested Citation

  • Phillips, Peter C.B. & Magdalinos, Tassos, 2013. "Inconsistent Var Regression With Common Explosive Roots," Econometric Theory, Cambridge University Press, vol. 29(4), pages 808-837, August.
  • Handle: RePEc:cup:etheor:v:29:y:2013:i:04:p:808-837_00
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    References listed on IDEAS

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    1. Phillips, Peter C B, 1985. "The Exact Distribution of LIML: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(1), pages 21-36, February.
    2. Anders Rygh Swensen, 2006. "Bootstrap Algorithms for Testing and Determining the Cointegration Rank in VAR Models -super-1," Econometrica, Econometric Society, vol. 74(6), pages 1699-1714, November.
    3. Giuseppe Cavaliere & Anders Rahbek & A. M. Robert Taylor, 2014. "Bootstrap Determination of the Co-Integration Rank in Heteroskedastic VAR Models," Econometric Reviews, Taylor & Francis Journals, vol. 33(5-6), pages 606-650, August.
    4. Fischer, Andreas M., 1993. "Weak exogeneity and dynamic stability in cointegrated VARs," Economics Letters, Elsevier, vol. 43(2), pages 167-170.
    5. 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.
    6. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    7. Cavaliere, Giuseppe & Rahbek, Anders & Taylor, A.M. Robert, 2010. "Cointegration Rank Testing Under Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1719-1760, December.
    8. Magdalinos, Tassos & Phillips, Peter C.B., 2009. "Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors," Econometric Theory, Cambridge University Press, vol. 25(2), pages 482-526, April.
    9. 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.
    10. Fanelli, Luca, 2007. "Present Value Relations, Granger Noncausality, And Var Stability," Econometric Theory, Cambridge University Press, vol. 23(6), pages 1254-1260, December.
    11. Phillips, Peter C.B. & Magdalinos, Tassos, 2008. "Limit Theory For Explosively Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 24(4), pages 865-887, August.
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    Cited by:

    1. repec:eee:econom:v:201:y:2017:i:2:p:400-416 is not listed on IDEAS
    2. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    3. Chen, Shyh-Wei & Hsu, Chi-Sheng & Xie, Zixong, 2016. "Are there periodically collapsing bubbles in the stock markets? New international evidence," Economic Modelling, Elsevier, vol. 52(PB), pages 442-451.
    4. Knight, John & Satchell, Stephen & Srivastava, Nandini, 2014. "Steady state distributions for models of locally explosive regimes: Existence and econometric implications," Economic Modelling, Elsevier, vol. 41(C), pages 281-288.

    More about this item

    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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