Hostname: page-component-89b8bd64d-mmrw7 Total loading time: 0 Render date: 2026-05-09T09:36:50.534Z Has data issue: false hasContentIssue false
  • English
  • Français

ANALYSIS OF COEXPLOSIVEPROCESSES

Published online by Cambridge University Press:  07 October 2009

Bent Nielsen
Get access Rights & Permissions [Opens in a new window]

Abstract

A vector autoregressive model allowing for unit rootsas well as an explosive characteristic root isdeveloped. The Granger-Johansen representation showsthat this results in processes with two commonfeatures: a random walk and an explosively growingprocess. Cointegrating and coexplosive vectors canbe found that eliminate these common factors. Thelikelihood ratio test for a simple hypothesis on thecoexplosive vectors is analyzed. The method isillustrated using data from the extreme Yugoslavianhyperinflation of the 1990s.

Information

Type
Research Article
Information
Econometric Theory , Volume 26 , Issue 3 , June 2010 , pp. 882 - 915
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

I am grateful to Søren Johansen, who read anearlier version of this paper very carefully andpresented it at the Conference on Common Featuresin Rio de Janeiro in July 2002. I have alsobenefited from discussions with Martin Wagner andinsightful comments from the referees.Computations were done using PcGive (Doornik andHendry, 2001). Financial support from ESRC grantRES-000-27-0179 is gratefully acknowledged.

References

REFERENCES

Anderson, T.W. (1959) On asymptotic distributions of estimates of parameters of stochastic difference equations. Annals of Mathematical Statistics 30, 676–687.CrossRefGoogle Scholar
Cagan, P. (1956) The monetary dynamics of hyper-inflation. In Friedman, M. (ed.), Studies in the Quantity Theory of Money, pp. 25–117. University of Chicago Press.Google Scholar
Chan, N.H. & Wei, C.Z. (1988) Limiting distributions of least squares estimates of unstable autoregressive processes. Annals of Statistics 16, 367–401.Google Scholar
Christiano, L.J. (1987) Cagan’s model of hyperinflation under rational expectations. International Economic Review 28, 33–49.CrossRefGoogle Scholar
Doornik, J.A. & Hendry, D.F. (2001) Empirical Econometric Modelling Using PcGive 10, vols. 1 and 2. Timberlake Consultants Press.Google Scholar
Duflo, M., Senoussi, R., & Touati, R. (1991) Propriétés asymptotiques presque sûre de l’estimateur des moindres carrés d’un modèle autorégressif vectoriel. Annales de l’Institut Henri Poincaré - Probabilités et Statistiques 27, 1–25.Google Scholar
Engler, E. & Nielsen, B. (2009) The empirical process of autoregressive residuals. Econometrics Journal 12, 367–381.Google Scholar
Engsted, T. (2006) Explosive bubbles in the cointegrated VAR model. Finance Research Letters 3, 154–162.CrossRefGoogle Scholar
Evans, P. (1978) Time series analysis of the German hyperinflation. International Economic Review 19, 195–209.Google Scholar
Johansen, S. (1988) Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 231–254.Google Scholar
Johansen, S. (1995) Likelihood-Based Inference in Cointegrated Vector Autoregressive Models. Oxford University Press.CrossRefGoogle Scholar
Johansen, S. (1997) Likelihood analysis of the I(2) model. Scandinavian Journal of Statistics 24, 433–462.10.1111/1467-9469.00074CrossRefGoogle Scholar
Johansen, S. (2002) A small sample correction for the test of cointegration rank in the vector autoregressive model. Econometrica 70, 1929–1962.Google Scholar
Johansen, S. & Schaumburg, E. (1999) Likelihood analysis of seasonal cointegration. Journal of Econometrics 88, 301–339.Google Scholar
Juselius, K. (2006) The Cointegrated VAR Model. Oxford University Press.Google Scholar
Juselius, K. & Mladenović, Z. (2002) High inflation, hyper inflation and explosive roots. The case of Jugoslavia. Mimeo, University of Copenhagen. http://www.econ.ku.dk/okokj/papers/hyper.pdf.Google Scholar
Lai, T.L. & Wei, C.Z. (1983) A note on martingale difference sequences satisfying the local Marcinkiewicz-Zygmund condition. Bulletin of the Institute of Mathematics, Academia Sinica 11, 1–13.Google Scholar
Lai, T.L. & Wei, C.Z. (1985) Asymptotic properties of multivariate weighted sums with applications to stochastic regression in linear dynamic systems. In Krishnaiah, P.R. (ed.), Multivariate Analysis VI, pp. 375–393. Elsevier Science Publishers.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.CrossRefGoogle Scholar
Nielsen, B. (2001) The asymptotic distribution of unit root tests of unstable autoregressive processes. Econometrica 69, 211–219.10.1111/1468-0262.00184Google Scholar
Nielsen, B. (2005) Strong consistency results for least squares statistics in general vector autoregressive models. Econometric Theory 21, 534–561.10.1017/S0266466605050310Google Scholar
Nielsen, B. (2006a) Correlograms for non-stationary autoregressions. Journal of the Royal Statistical Society B68, 707–720.CrossRefGoogle Scholar
Nielsen, B. (2006b) Order determination in general vector autoregressions. In Ho, H.-C., Ing, C.-K., & Lai, T.L. (eds.), Time Series and Related Topics: In Memory of Ching-Zong Wei. IMS Lecture Notes and Monograph Series 52, 93–112.CrossRefGoogle Scholar
Nielsen, B. (2008a) On the explosive nature of hyper-inflation data. Economics: The Open-Access, Open-Assessment E-Journal 2, 2008–21.Google Scholar
Nielsen, B. (2008b) Singular Vector Autoregressions with Deterministic Terms: Strong Consistency and Lag Order Determination. Discussion paper, Nuffield College.Google Scholar
Petrović, P., Bogetić, Ž., & Vujošević, Z. (1999) The Yugoslav hyper-inflation of 1992-1994: Causes, dynamics, and money supply process. Journal of Comparative Economics 27, 335–353.Google Scholar
Petrović, P. & Mladenović, Z. (2000) Money demand and exchange rate determination under hyper-inflation: Conceptual issues and evidence from Yugoslavia. Journal of Money, Credit, and Banking 32, 785–806.CrossRefGoogle Scholar
Petrović, P. & Vujošević, Z. (1996) The monetary dynamics in the Yugoslav hyper-inflation of 1991-1993: The Cagan money demand. European Journal of Political Economy 12, 467–483. Erratum (1997) in vol. 13, 385–387.Google Scholar
Phillips, P.C.B. & Magdalinos, T. (2008) Limit theory for explosively cointegrated systems. Econometric Theory 24, 865–887.10.1017/S0266466608080353Google Scholar
Rahbek, A., Kongsted, H.C. & Jørgensen, C. (1999) Trend stationarity in the I(2) cointegration model. Journal of Econometrics 90, 265–289.Google Scholar
Sargent, T. (1977) The demand for money during hyperinflations under rational expectations: I. International Economic Review 18, 59–82.Google Scholar
Sargent, T. & Wallace, N. (1973) Rational expectations and the dynamics of hyperinflation. International Economic Review 14, 328–350.10.2307/2525924Google Scholar
Taylor, M.P. (1991) The hyper-inflation model of money demand revisited. Journal of Money, Credit, and Banking 23, 327–351.10.2307/1992749Google Scholar