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Abstract:
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The existence of features such as persistence, co-integration, and reduced dimensional dynamics have made the analysis of vector autoregressive (VAR) series exciting, and has generated a vast literature on unit root, co-integrated and educed rank VAR systems. In co-integrated vector autoregressive models, the root structure is a mixture of stable roots and unit roots. A common practice in co-integrated processes has been to study dynamics driven by the stable roots after differencing the data to remove the unit roots. However, there is no clear guidelines on when to difference the data and when to use models with the levels of the economic variables. Also, properly parametrizing the stable portion of a VAR polynomial is particularly important for prior specification in Bayesian VAR, which has become a popular tool for analyzing large systems of macroeconomic series. We provide an exact parameterization that enables one to optimally difference a co-integrated system and thereby avoids unwanted features such as non-invertibility that arise from over-differencing. We illustrate the usefulness of our proposal through a macroeconomic example.
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