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Limit Theory For Cointegrated Systems With Moderately Integrated And Moderately Explosive Regressors

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

Abstract

An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form ρ = 1 + c / n , involving moderate deviations from unity when α null (0, 1) and c null null are constant parameters. When the data are moderately integrated in the stationary direction (with c c > 0) the limit theory is mixed normal with Cauchy-type tail behavior, and the rate of convergence is explosive, as in the case of a moderately explosive scalar autoregression (Phillips and Magdalinos, 2007, Journal of Econometrics 136, 115–130). Moreover, the limit theory applies without any distributional assumptions and for weakly dependent errors under conventional moment conditions, so an invariance principle holds, unlike the well-known case of an explosive autoregression. This theory validates inference in cointegrating regression with mildly explosive regressors. The special case in which the regressors themselves have a common explosive component is also considered.

Suggested Citation

  • 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(02), pages 482-526, April.
  • Handle: RePEc:cup:etheor:v:25:y:2009:i:02:p:482-526_09
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    1. repec:eee:econom:v:201:y:2017:i:2:p:400-416 is not listed on IDEAS
    2. Breitung, Jörg & Demetrescu, Matei, 2015. "Instrumental variable and variable addition based inference in predictive regressions," Journal of Econometrics, Elsevier, vol. 187(1), pages 358-375.
    3. Phillips, Peter C.B. & Magdalinos, Tassos, 2013. "Inconsistent Var Regression With Common Explosive Roots," Econometric Theory, Cambridge University Press, vol. 29(04), pages 808-837, August.
    4. Li, Jian & Chavas, Jean-Paul & Etienne, Xiaoli & Li, Chongguang, 2016. "Commodity Price Bubbles and Macroeconomics: Evidence from Chinese Agricultural Markets," 2016 Annual Meeting, July 31-August 2, 2016, Boston, Massachusetts 235068, Agricultural and Applied Economics Association.
    5. Westerlund J. & Smeekes S., 2013. "Robust block bootstrap panel predictability tests," Research Memorandum 060, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Peter C.B. Phillips & Ye Chen, "undated". "Restricted Likelihood Ratio Tests in Predictive Regression," Cowles Foundation Discussion Papers 1968, Cowles Foundation for Research in Economics, Yale University.
    7. 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.
    8. Peter C. B. Phillips & Sainan Jin, 2014. "Testing the Martingale Hypothesis," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 537-554, October.
    9. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    10. Phillips, Peter C.B. & Lee, Ji Hyung, 2013. "Predictive regression under various degrees of persistence and robust long-horizon regression," Journal of Econometrics, Elsevier, vol. 177(2), pages 250-264.
    11. 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.
    12. Tassos Magdalinos, 2008. "Mildly explosive autoregression under weak and strong dependence," Discussion Papers 08/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    13. repec:eee:finlet:v:23:y:2017:i:c:p:96-102 is not listed on IDEAS
    14. Demetrescu, Matei, 2014. "Enhancing the local power of IVX-based tests in predictive regressions," Economics Letters, Elsevier, vol. 124(2), pages 269-273.
    15. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.

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