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MIXED NORMAL INFERENCE ON MULTICOINTEGRATION

Published online by Cambridge University Press:  06 April 2010

H. Peter Boswijk
H. Peter Boswijk*
Affiliation:
University of Amsterdam
*
*Address correspondence to H. Peter Boswijk, Department of Quantitative Economics, University of Amsterdam, Roetersstraat 11, NL-1018 WB Amsterdam, The Netherlands; e-mail: h.p.boswijk@uva.nl.
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Abstract

Asymptotic likelihood analysis of cointegration in I (2) models (see Johansen, 1997, 2006; Boswijk, 2000; Paruolo, 2000) has shown that inference on most parameters is mixed normal, implying hypothesis test statistics with an asymptotic χ2 null distribution. The asymptotic distribution of the multicointegration parameter estimator so far has been characterized by a Brownian motion functional, which has been conjectured to have a mixed normal distribution, based on simulations. The present note proves this conjecture.

Information

Type
NOTES AND PROBLEMS
Information
Econometric Theory , Volume 26 , Issue 5 , October 2010 , pp. 1565 - 1576
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Boswijk, H.P. (2000) Mixed normality and ancillarity in I (2) systems. Econometric Theory 16, 878–904.Google Scholar
Engsted, T. & Johansen, S. (1999) Granger’s representation theorem and multicointegration. In Engle, R.F. & White, H. (eds.), Cointegration, Causality and Forecasting: Festschrift in Honour of Clive Granger, pp. 200–212. Oxford University Press.Google Scholar
Granger, C.W.J. (1986) Developments in the study of cointegrated economic variables. Oxford Bulletin of Economics and Statistics 48, 213–228.Google Scholar
Granger, C.W.J. & Lee, T.-H. (1990) Multicointegration. In Rhodes, G.F. Jr. & Fomby, T.B. (eds.), Advances in Econometrics: Cointegration, Spurious Regressions and Unit Roots. pp. 71–84. JAI Press.Google Scholar
Johansen, S. (1992) A representation of vector autoregressive processes integrated of order 2. Econometric Theory 8, 188–202.Google Scholar
Johansen, S. (1997) Likelihood analysis of the I (2) model. Scandinavian Journal of Statistics 24, 433–462.Google Scholar
Johansen, S. (2006) Statistical analysis of hypotheses on the cointegrating relations in the I (2) model. Journal of Econometrics 132, 81–115.Google Scholar
Magnus, J.R. & Neudecker, H. (1988) Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley.Google Scholar
Mosconi, R. & Paruolo, P. (2010) Identification of cointegrating relations in I (2) vector autoregressive models. Working paper, University of Insubria.Google Scholar
Paruolo, P. (1995) Topics in Statistical Inference for Vector Autoregressive Processes Integrated of Order 1 and 2. PhD thesis, University of Copenhagen.Google Scholar
Paruolo, P. (2000) Asymptotic efficiency of the two stage estimator in I (2) systems. Econometric Theory 16, 524–550.Google Scholar
Paruolo, P. & Rahbek, A. (1999) Weak exogeneity in I (2) VAR systems. Journal of Econometrics 93, 281–308.CrossRefGoogle 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
Tanaka, K. (1996) Time Series Analysis. Nonstationary and Noninvertible Distribution Theory. Wiley.Google Scholar