Christian Jobelius Schulz, Christoph Hanck, Simon Hirsch, Florian Ziel
arXiv 16 Oct 2026 · Statistics — Methodology
arXiv:2610.23119 · PDF · Extracted main text
We propose an online multivariate distributional forecasting model in which we condition the parameters of a vine copula on covariates. An online algorithm updates the parameters sequentially using only the most recent observations. Existing approaches require full batch re-estimation using all available data at each update step, which makes them computationally slow in large-scale forecasting applications and less suitable for settings in which dependence structures change over time. Simulation results show that the online procedure achieves forecasting performance comparable to that of the batch estimator, while reducing computation time substantially. We illustrate the method in a forecasting application to electricity net-demand across five regions of Great Britain and show that (i) the conditional vine copula model outperforms unconditional Gaussian and vine copula benchmarks and (ii) that online estimation improves forecast accuracy when batch re-estimation is not available. The algorithm is implemented in the Python package ondil.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Gioia, V., Fasiolo, M., Browell, J., and Bellio, R (2025) Additive covariance matrix models: modeling regional electricity net-demand in great britain | 1.000 | 11 | 3 | 100% |
| 2 | Jobst, D., Möller, A., and Gro, J (2024) Gradient-boosted generalized linear models for conditional vine copulas | 1.000 | 9 | 3 | 100% |
| 3 | Vatter, T. and Nagler, T (2018) Generalized additive models for pair-copula constructions | 1.000 | 5 | 3 | 100% |
| 4 | Hirsch, S., Berrisch, J., and Ziel, F (2024) Online distributional regression self | 0.843 | 3 | 3 | 100% |
| 5 | Hirsch, S (2025) Online multivariate regularized distributional regression for high-dimensional probabilistic electricity price forecasting self | 0.811 | 4 | 2 | 100% |
| 6 | Angelosante, D., Bazerque, J. A., and Giannakis, G. B (2010) Online adaptive estimation of sparse signals: Where rls meets the $_1$-norm | 0.737 | 4 | 3 | 50% |
| 7 | Friedman, J., Hastie, T., Höfling, H., and Tibshirani, R (2007) Pathwise coordinate optimization | 0.737 | 4 | 3 | 50% |
| 8 | Messner, J. W. and Pinson, P (2019) Online adaptive lasso estimation in vector autoregressive models for high dimensional wind power forecasting | 0.737 | 4 | 3 | 50% |
| 9 | Hansen, P. R., Lunde, A., and Nason, J. M (2011) The model confidence set | 0.737 | 3 | 2 | 100% |
| 10 | Aas, K., Czado, C., Frigessi, A., and Bakken, H (2009) Pair-copula constructions of multiple dependence | 0.644 | 2 | 2 | 100% |
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