Nonlinear Fore(Back)casting and Innovation Filtering for Causal-Noncausal VAR Models
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Gourieroux, Christian Jasiak, Joann |
| author_facet | Gourieroux, Christian Jasiak, Joann |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09922 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Nonlinear Fore(Back)casting and Innovation Filtering for Causal-Noncausal VAR Models Gourieroux, Christian Jasiak, Joann Econometrics 62G, 62H, 62P20, 62M10 I.6.3; I.6.4 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. |
| title | Nonlinear Fore(Back)casting and Innovation Filtering for Causal-Noncausal VAR Models |
| topic | Econometrics 62G, 62H, 62P20, 62M10 I.6.3; I.6.4 |
| url | https://arxiv.org/abs/2205.09922 |