Hostname: page-component-74656f9884-rdgjk Total loading time: 0 Render date: 2026-11-09T02:56:32.169Z Has data issue: false hasContentIssue false
  • English
  • Français

INCONSISTENT VAR REGRESSION WITH COMMON EXPLOSIVE ROOTS

Published online by Cambridge University Press:  16 January 2013

Peter C.B. Phillips  and
Tassos Magdalinos
Peter C.B. Phillips*
Affiliation:
Yale University, University of Auckland, University of Southampton, and Singapore Management University
Tassos Magdalinos
Affiliation:
University of Southampton
*
*Address correspondence to Peter Phillips, Cowles Foundation for Research in Economics, Yale University, Box 208281, New Haven, CT 06520-8281, USA; e-mail: peter.phillips@yale.edu..
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

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.

Information

Type
ARTICLES
Information
Econometric Theory , Volume 29 , Issue 4 , August 2013 , pp. 808 - 837
Copyright
Copyright © Cambridge University Press 2013 

References

REFERENCES

Anderson, T.W. (1959) On asymptotic distributions of estimates of parameters of stochastic difference equations. Annals of Mathematical Statistics 30, 676–687.Google Scholar
Cavaliere, G., Rahbek, A., & Taylor, A.M.R. (2010) Co-integration rank testing under conditional heteroskedasticity. Econometric Theory 26, 1719–1760.Google Scholar
Cavaliere, G., Rahbek, A., & Taylor, A.M.R. (2012) Bootstrap determination of the co-integration rank in VAR models. Econometrica 80, 1721–1740.Google Scholar
Engle, R.F., Hendry, D.F., & Richard, J.-F. (1983) Exogeneity. Econometrica 51, 277–304.CrossRefGoogle Scholar
Fanelli, L. (2007) Present value relations, Granger noncausality, and VAR stability. Econometric Theory 23, 1254–1260.CrossRefGoogle Scholar
Fischer, A.M. (1993) Weak exogeneity and dynamic stability in cointegrated VARs. Economics Letters 43, 167–170.Google Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Application. Academic Press.Google Scholar
Lai, T.L. & Wei, C.Z. (1982) Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Annals of Statistics 10, 154–166.Google Scholar
Lai, T.L. & Wei, C.Z. (1983) A note on martingale difference sequences satisfying the local Marcinkiewich-Zygmund condition. Bulletin of the Institute of Mathematics Academia Sinica 11, 1–13.Google Scholar
Luati, A. & Paruolo, P. (2002) Sulla distribuzione di una base di norma unitaria del complemento ortogonale di un vettore gaussiano: Il caso bidimensionale. Statistica LXII, 33–38.Google Scholar
Magdalinos, T. & Phillips, P.C.B. (2009) Limit theory for cointegrated systems with moderately integrated and moderately explosive regressors. Econometric Theory 25, 482–526.Google Scholar
Nielsen, B. (2009) Singular Vector Autoregressions with Deterministic Terms: Strong Consistency and Lag Order Determination. Working paper, University of Oxford.Google Scholar
Park, J.Y. & Phillips, P.C.B. (1988) Statistical inference in regressions with integrated processes: Part 1. Econometric Theory 4, 468–497.Google Scholar
Park, J.Y. & Phillips, P.C.B. (1989) Statistical inference in regressions with integrated processes: Part 2. Econometric Theory 5, 95–131.Google Scholar
Phillips, P.C.B. (1984) The exact distribution of LIML: I. International Economic Review 25, 249–261.Google Scholar
Phillips, P.C.B. & Magdalinos, T. (2007) Limit theory for moderate deviations from a unit root. Journal of Econometrics 136, 115–130.Google Scholar
Phillips, P.C.B. & Magdalinos, T. (2008) Limit theory for explosively cointegrated systems. Econometric Theory 24, 865–887.Google Scholar
Phillips, P.C.B., Wu, Y., & Yu, J. (2011) Explosive behavior in the 1990s Nasdaq: When did exuberance escalate asset values? International Economic Review 52, 201–226.CrossRefGoogle Scholar
Phillips, P.C.B. & Yu, J. (2011) Dating the timeline of financial bubbles during the subprime crisis. Quantitative Economics 2, 455–491.Google Scholar
Stout, W.F. (1974) Almost Sure Convergence. Academic Press.Google Scholar
Swensen, A.R. (2006) Bootstrap algorithms for testing and determining the cointegration rank in VAR models. Econometrica 74, 1699–1714.Google Scholar