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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 introduce closed-form formulas of out-of-sample predictive densities for forecasting and backcasting of mixed causal-noncausal (Structural) Vector Autoregressive VAR models. These nonlinear and time irreversible non-Gaussian VAR processes are shown to satisfy the Markov property in both calendar and reverse time. A post-estimation inference method for assessing the forecast interval uncertainty due to the preliminary estimation step is introduced too. The nonlinear past-dependent innovations of a mixed causal-noncausal VAR model are defined and their filtering and identification methods are discussed. Our approach is illustrated by a simulation study, and an application to cryptocurrency prices.

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 Apr 2024.
    • 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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