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

Christian Gourieroux; Joann Jasiak

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arXiv · 2205.09922

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

Christian Gourieroux·Joann Jasiak

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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.

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BibTeX RIS

Christian Gourieroux, Joann Jasiak. 2022-05-20. Nonlinear Fore(Back)casting and Innovation Filtering for Causal-Noncausal VAR Models. https://arxiv.org/abs/2205.09922

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