Moving Aggregate Modified Autoregressive Copula-Based Time Series Models (MAGMAR-Copulas)
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914413822345216 |
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| author | Pappert, Sven |
| author_facet | Pappert, Sven |
| contents | Copula-based time series models can model univariate and stationary time series in a flexible way by decomposing the joint distribution of consecutive observations into a copula and the stationary distribution. Implicitly this approach assumes a finite Markov order. In reality a time series may not follow the Markov property. We modify the copula-based time series models by introducing a moving aggregate (MAG) part into the model updating equation. The functional form of the MAG-part is given as the conditional quantile function corresponding to a copula. The resulting MAG-modified Autoregressive Copula-Based Time Series model (MAGMAR-Copula) is discussed in detail and distributional properties are derived in a D-vine framework. We show that the stationary distribution implied by the model is not standard-uniform. Hence we propose an adjustment transformation that recovers the desired standard-uniformity. The model nests the classical ARMA model and can be interpreted as a non-linear generalization of the ARMA model. The modeling performance is evaluated by modeling US inflation. Our model is competitive with benchmark models in terms of information criteria. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01491 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moving Aggregate Modified Autoregressive Copula-Based Time Series Models (MAGMAR-Copulas) Pappert, Sven Methodology Probability Statistics Theory Applications Copula-based time series models can model univariate and stationary time series in a flexible way by decomposing the joint distribution of consecutive observations into a copula and the stationary distribution. Implicitly this approach assumes a finite Markov order. In reality a time series may not follow the Markov property. We modify the copula-based time series models by introducing a moving aggregate (MAG) part into the model updating equation. The functional form of the MAG-part is given as the conditional quantile function corresponding to a copula. The resulting MAG-modified Autoregressive Copula-Based Time Series model (MAGMAR-Copula) is discussed in detail and distributional properties are derived in a D-vine framework. We show that the stationary distribution implied by the model is not standard-uniform. Hence we propose an adjustment transformation that recovers the desired standard-uniformity. The model nests the classical ARMA model and can be interpreted as a non-linear generalization of the ARMA model. The modeling performance is evaluated by modeling US inflation. Our model is competitive with benchmark models in terms of information criteria. |
| title | Moving Aggregate Modified Autoregressive Copula-Based Time Series Models (MAGMAR-Copulas) |
| topic | Methodology Probability Statistics Theory Applications |
| url | https://arxiv.org/abs/2402.01491 |