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

Christian Gourieroux and Joann Jasiak

Papers from arXiv.org

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.

Date: 2022-05, Revised 2025-07
New Economics Papers: this item is included in nep-dem, nep-ecm, nep-ets and nep-for
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