Rolling-Origin Conformal Prediction under Local Stationarity and Weak Dependence
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| Format: | Preprint |
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2026
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| author | Halkiewicz, Stanisław M. S. |
| author_facet | Halkiewicz, Stanisław M. S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_08422 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rolling-Origin Conformal Prediction under Local Stationarity and Weak Dependence Halkiewicz, Stanisław M. S. Methodology Econometrics Computation 62G15, 62M10, 62G08 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. |
| title | Rolling-Origin Conformal Prediction under Local Stationarity and Weak Dependence |
| topic | Methodology Econometrics Computation 62G15, 62M10, 62G08 |
| url | https://arxiv.org/abs/2605.08422 |