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Identifiability of Structural Singular Vector Autoregressive Models

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  • Bernd Funovits
  • Alexander Braumann

Abstract

We generalize well-known results on structural identifiability of vector autoregressive models (VAR) to the case where the innovation covariance matrix has reduced rank. Structural singular VAR models appear, for example, as solutions of rational expectation models where the number of shocks is usually smaller than the number of endogenous variables, and as an essential building block in dynamic factor models. We show that order conditions for identifiability are misleading in the singular case and provide a rank condition for identifiability of the noise parameters. Since the Yule-Walker equations may have multiple solutions, we analyze the effect of restrictions on the system parameters on over- and underidentification in detail and provide easily verifiable conditions.

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  • Bernd Funovits & Alexander Braumann, 2019. "Identifiability of Structural Singular Vector Autoregressive Models," Papers 1910.04096, arXiv.org, revised Oct 2020.
    • Handle: RePEc:arx:papers:1910.04096
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    References listed on IDEAS

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    1. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
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    8. Weitian Chen & Brian D.O. Anderson & Manfred Deistler & Alexander Filler, 2011. "Solutions of Yule‐Walker equations for singular AR processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(5), pages 531-538, September.
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