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

Christian Gourieroux and Joann Jasiak

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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.

Date: 2022-05, Revised 2024-04
New Economics Papers: this item is included in nep-dem, nep-ecm, nep-ets and nep-for
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