Christian Gourieroux, Joann Jasiak
arXiv 20 May 2022 · Econometrics · publishedJournal of Financial Econometrics (2026) · 7 citations (OpenAlex)
arXiv:2205.09922 · PDF · DOI · OpenAlex · Extracted main text
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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