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Analyzing I(2) Systems by Transformed Vector Autoregressions


  • Hans Christian Kongsted

    (Institute of Economics, University of Copenhagen)

  • Heino Bohn Nielsen

    (Institute of Economics, University of Copenhagen)


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.

Suggested Citation

  • Hans Christian Kongsted & Heino Bohn Nielsen, 2002. "Analyzing I(2) Systems by Transformed Vector Autoregressions," Discussion Papers 02-20, University of Copenhagen. Department of Economics.
  • Handle: RePEc:kud:kuiedp:0220

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    Cited by:

    1. Kongsted, Hans Christian, 2005. "Testing the nominal-to-real transformation," Journal of Econometrics, Elsevier, vol. 124(2), pages 205-225, February.

    More about this item


    cointegration; stochastic trend; price homogeneity; nominal; real; Monte Carlo experiment;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics

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