arXiv 5 Oct 2024 · Statistics — Methodology · publishedJournal of Business and Economic Statistics (2026)
arXiv:2410.04165 · PDF · DOI · OpenAlex · Extracted main text
This paper lays out a principled approach to compare copula forecasts via strictly consistent scores. We first establish the negative result that, in general, copulas fail to be elicitable, implying that copula predictions cannot sensibly be compared on their own. A notable exception is on Fr\'echet classes, that is, when the marginal distribution structure is given and fixed, in which case we give suitable scores for the copula forecast comparison. As a remedy for the general non-elicitability of copulas, we establish novel multi-objective scores for copula forecast along with marginal forecasts. They give rise to two-step tests of equal or superior predictive ability which admit attribution of the forecast ranking to the accuracy of the copulas or the marginals. Simulations show that our two-step tests work well in terms of size and power. We illustrate our new methodology via an empirical example using copula forecasts for international stock market indices.
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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 | Fissler, T. and Hoga, Y (2024) Backtesting systemic risk forecasts using multi-objective elicitability self | 1.000 | 7 | 3 | 100% |
| 2 | Gneiting, T (2011) Making and evaluating point forecasts | 1.000 | 6 | 3 | 100% |
| 3 | Diebold, F. X. and Mariano, R. S (1995) Comparing predictive accuracy | 1.000 | 5 | 4 | 100% |
| 4 | Giacomini, R. and White, H (2006) Tests of conditional predictive ability | 0.843 | 4 | 3 | 75% |
| 5 | Creal, D., Koopman, S. J., and Lucas, A (2013) Generalized autoregressive score models with applications | 0.811 | 4 | 2 | 100% |
| 6 | Osband, K. H (1985) Providing Incentives for Better Cost Forecasting | 0.811 | 4 | 2 | 100% |
| 7 | Sklar, A (1959) Fonctions de répartition à $n$ dimensions et leurs marges | 0.811 | 4 | 2 | 100% |
| 8 | Gneiting, T. and Raftery, A. E (2007) Strictly proper scoring rules, prediction, and estimation | 0.737 | 3 | 2 | 100% |
| 9 | Chen, X. and Fan, Y (2006) Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification | 0.644 | 2 | 2 | 100% |
| 10 | Coroneo, L. and Iacone, F (2020) Comparing predictive accuracy in small samples using fixed-smoothing asymptotics | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 42 scored citations.