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The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model

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  • Søren Johansen

Abstract

. We show that the asymptotic distribution of the estimated stationary roots in a vector autoregressive model is Gaussian. A simple expression for the asymptotic variance in terms of the roots and the eigenvectors of the companion matrix is derived. The results are extended to the cointegrated vector autoregressive model and we discuss the implementation of the results for complex roots.

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  • Søren Johansen, 2003. "The asymptotic variance of the estimated roots in a cointegrated vector autoregressive model," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 663-678, November.
    • Handle: RePEc:bla:jtsera:v:24:y:2003:i:6:p:663-678
    DOI: 10.1111/j.1467-9892.2003.00328.x
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    1. Johansen, Soren & Schaumburg, Ernst, 1998. "Likelihood analysis of seasonal cointegration," Journal of Econometrics, Elsevier, vol. 88(2), pages 301-339, November.
    2. Wymer, C R, 1972. "Econometric Estimation of Stochastic Differential Equation Systems," Econometrica, Econometric Society, vol. 40(3), pages 565-577, May.
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    Cited by:

    1. Mauricio, Jose Alberto, 2006. "Exact maximum likelihood estimation of partially nonstationary vector ARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3644-3662, August.
    2. Bent Nielsen & Heino Bohn Nielsen, 2008. "Properties of etimated characteristic roots," Economics Papers 2008-W07, Economics Group, Nuffield College, University of Oxford.
    3. Onatski, Alexei & Uhlig, Harald, 2012. "Unit Roots In White Noise," Econometric Theory, Cambridge University Press, vol. 28(3), pages 485-508, June.
    4. Alain Hecq & Franz Palm & Jean-Pierre Urbain, 2002. "Separation, Weak Exogeneity, And P-T Decomposition In Cointegrated Var Systems With Common Features," Econometric Reviews, Taylor & Francis Journals, vol. 21(3), pages 273-307.

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