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Nonlinear Fore(Back)casting and Innovation Filtering for Causal-Noncausal VAR Models

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  • Christian Gourieroux
  • Joann Jasiak

Abstract

We show that the mixed causal-noncausal Vector Autoregressive (VAR) processes satisfy the Markov property in both calendar and reverse time. Based on that property, we introduce closed-form formulas of forward and backward predictive densities for point and interval forecasting and backcasting out-of-sample. The backcasting formula is used for adjusting the forecast interval to obtain a desired coverage level when the tail quantiles are difficult to estimate. A confidence set for the prediction interval is introduced for assessing the uncertainty due to estimation. We also define new nonlinear past-dependent innovations of mixed causal-noncausal VAR models for impulse response function analysis. Our approach is illustrated by simulations and an application to oil prices and real GDP growth rates.

Suggested Citation

  • Christian Gourieroux & Joann Jasiak, 2022. "Nonlinear Fore(Back)casting and Innovation Filtering for Causal-Noncausal VAR Models," Papers 2205.09922, arXiv.org, revised Jul 2025.
    • Handle: RePEc:arx:papers:2205.09922
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    Cited by:

    1. Francesco Giancaterini & Alain Hecq & Claudio Morana, 2022. "Is Climate Change Time-Reversible?," Econometrics, MDPI, vol. 10(4), pages 1-18, December.
    2. Gianluca Cubadda & Francesco Giancaterini & Alain Hecq & Joann Jasiak, 2023. "Optimization of the Generalized Covariance Estimator in Noncausal Processes," Papers 2306.14653, arXiv.org, revised Jan 2024.

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