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Analysing I(2) Systems by Transformed Vector Autoregressions

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  • Hans Christian Kongsted
  • Heino Bohn Nielsen

Abstract

We characterize the restrictions imposed by the minimal I(2)‐to‐I(1) transformation that underlies much applied work, e.g. on money demand relationships or open‐economy pricing relationships. The relationship between the parameters of the original I(2) vector autoregression, including the coefficients of polynomially cointegrating relationships, and the transformed I(1) model is characterized. We discuss estimation of the transformed model subject to restrictions as well as the more commonly used approach of unrestricted reduced rank regression. Only a minor loss of efficiency is incurred by ignoring the restrictions in the empirical example and a simulation study. A properly transformed vector autoregression thus provides a practical and effective means for inference on the parameters of the I(2) model.

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  • Hans Christian Kongsted & Heino Bohn Nielsen, 2004. "Analysing I(2) Systems by Transformed Vector Autoregressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(3), pages 379-397, July.
  • Handle: RePEc:bla:obuest:v:66:y:2004:i:3:p:379-397
    DOI: 10.1111/j.1468-0084.2004.00084.x
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    7. Assenmacher-Wesche, Katrin & Beyer, Andreas, 2019. "A cointegration model of money and wealth," CFS Working Paper Series 619, Center for Financial Studies (CFS).
    8. Nevin Cavusoglu & Michael D. Goldberg & Joshua Stillwagon, 2019. "New Evidence on the Portfolio Balance Approach to Currency Returns," Working Papers Series 89, Institute for New Economic Thinking.
    9. Johansen, Søren & Juselius, Katarina & Frydman, Roman & Goldberg, Michael, 2010. "Testing hypotheses in an I(2) model with piecewise linear trends. An analysis of the persistent long swings in the Dmk/$ rate," Journal of Econometrics, Elsevier, vol. 158(1), pages 117-129, September.

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