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Long-run risk in stationary vector autoregressive models

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  • Gourieroux, Christian
  • Jasiak, Joann

Abstract

This paper introduces a local-to-unity/small sigma model for stationary processes with long-range persistence and non-negligible long-run prediction and estimation risks. The model represents a process containing unobserved short and long-run components measured on different time scales. The short-run component is defined in calendar time, while the long-run component evolves in rescaled time with ultra-long units. We develop estimation and long-run prediction methods for time series with multivariate Vector Autoregressive (VAR) short-run components and reveal the impossibility of estimating consistently some of the long-run parameters, which causes significant estimation and prediction risks in the long run. A simulation study and an application to macroeconomic data illustrate the approach.

Suggested Citation

  • Gourieroux, Christian & Jasiak, Joann, 2025. "Long-run risk in stationary vector autoregressive models," Journal of Econometrics, Elsevier, vol. 248(C).
    • Handle: RePEc:eee:econom:v:248:y:2025:i:c:s0304407624002562
    DOI: 10.1016/j.jeconom.2024.105905
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