arXiv 8 May 2026 · Statistics — Methodology
arXiv:2605.08422 · PDF · DOI · OpenAlex · Extracted main text
We propose and analyse rolling-origin conformal prediction for time-series forecasting. The method calibrates the conformal quantile against the $m$ most recent pseudo-out-of-sample forecast errors, adapting to serial dependence, volatility clustering, and distributional drift that invalidate classical conformal guarantees. Under Hölder-$β$ local stationarity and $α$-mixing, we establish a four-term coverage-error decomposition and derive the optimal calibration window $m^{\star} \asymp T^{2β/(2β+1)}$ with coverage-error rate $O(T^{-β/(2β+1)})$. A Le Cam two-point construction shows this rate is minimax-optimal over the Hölder-$β$ model class. The Bahadur representation is proved under both $α$-mixing and the physical-dependence framework of Wu (2005). An oracle inequality formalises Winkler cross-validation as an adaptive window selector; the required uniform concentration condition is established in an appendix. Validation on six real series and 93 M4 competition series confirms the theory: rolling-origin calibration outperforms full-history calibration in 86% of comparisons (median Winkler improvement 12.3%), maintains coverage within $\pm2%$ of the 90% target at short and medium horizons, and the cross-frequency log-log regression slope $0.614$ ($95%$ CI $[0.424, 0.805]$) is consistent with the theoretical $2/3$ after controlling for frequency fixed effects.
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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 | Fryzlewicz P, Subba Rao S (2011) Mixing properties of ARCH and time-varying ARCH processes | 0.928 | 5 | 4 | 80% |
| 2 | Rio E (1993) Covariance inequalities for strongly mixing processes | 0.843 | 4 | 3 | 75% |
| 3 | Merlevède F, Peligrad M, Rio E (2009) Bernstein inequality and moderate deviations under strong mixing conditions | 0.737 | 4 | 4 | 50% |
| 4 | Zhou Z, Wu WB (2009) Local linear quantile estimation for nonstationary time series | 0.737 | 4 | 3 | 50% |
| 5 | Dahlhaus R (1997) Fitting time series models to nonstationary processes | 0.737 | 3 | 2 | 100% |
| 6 | Wu WB (2005) Nonlinear system theory: another look at dependence | 0.737 | 3 | 2 | 100% |
| 7 | Gibbs I, Candès E (2021) Adaptive conformal inference under distribution shift | 0.644 | 2 | 2 | 100% |
| 8 | Vovk V, Gammerman A, Shafer G (2005) Algorithmic Learning in a Random World | 0.644 | 2 | 2 | 100% |
| 9 | Winkler RL (1972) A decision theoretic approach to interval estimation | 0.644 | 2 | 2 | 100% |
| 10 | Vogt M (2012) Nonparametric regression for locally stationary time series | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 23 scored citations.