Rollcast: Proper-Score Gated Rolling Anchors for Adaptive Probabilistic Time-Series Forecasting

Giancarlo Vercellino

stat.MLSep 3, 2026

Rollcast: Proper-Score Gated Rolling Anchors for Adaptive Probabilistic Time-Series Forecasting

Authors: Giancarlo Vercellino

Organizations: Independent Researcher

Abstract

Rollcast is a probabilistic forecasting method for univariate time series that combines a compact set of rolling statistical anchors rather than relying on a single global model. Rolling means, medians, extrema, regression endpoints, and quantiles define candidate forecast locations and a representation of the current state. A state-dependent softmax gate learns anchor probabilities by minimizing negative log predictive density, while residual distributions retrieved from similar historical states provide local uncertainty. Recursive simulation propagates the resulting mixture over multiple forecast horizons. The method is evaluated in a Monte Carlo study covering eight data-generating processes, including autoregressive, random-walk, local-trend, threshold, regime-switching, stochastic-volatility, heavy-tailed, and variance-break dynamics. Across 2,000 independent fitted series, Rollcast is compared with the true conditional predictive distribution generated by an oracle simulator. Overall empirical coverage is 86.2% for nominal 90% intervals and 91.5% for nominal 95% intervals. Predictive intervals are on average 13.6% wider than the oracle at the 90% level, while CRPS is 14.4% higher than oracle CRPS. Performance is closest to the oracle under autoregressive, threshold, stochastic-volatility, heavy-tailed, and variance-break dynamics, while local trends and regime switching are more challenging. The results indicate that Rollcast can construct competitive probabilistic forecasts from simple, interpretable local summaries, while also identifying limitations in calibration and recursive uncertainty propagation.

Figures & tables

Parameter	Default candidate values
Rolling window $W$	20, 30, 45, 60, 90, 120
Responsibility temperature $\tau$	0.15, 0.25, 0.40
Gate penalty $\lambda$	0.001, 0.01, 0.05
Nearest states $K$	20, 40, 80
State bandwidth $h_{x}$	0.60, 1.00, 1.60
Residual bandwidth $h_{e}$	0.20, 0.35, 0.55

Table 1: Reference search spaces in the supplied implementation. A scalar value fixes the parameter; a vector triggers staged search.

DGP	Mechanism
Gaussian AR(1)	$y_{t}=0.70y_{t-1}+\varepsilon_{t}$ .
Gaussian random walk	$y_{t}=y_{t-1}+\varepsilon_{t}$ .
Local trend	$d_{t}=0.85d_{t-1}+0.15\eta_{t}$ , $y_{t}=y_{t-1}+d_{t}+0.50\varepsilon_{t}$ .
Threshold AR	$y_{t}=\phi(y_{t-1})y_{t-1}+\varepsilon_{t}$ , with $\phi=0.85$ above zero and $0.20$ otherwise.
Markov switching	Two regimes with $(\mu_{s},\phi_{s},\sigma_{s})=(-1.5,0.30,0.60)$ and $(1.5,0.80,1.50)$ , with transition matrix $\left(\begin{smallmatrix}0.95&0.05\\ 0.08&0.92\end{smallmatrix}\right)$ .
Stochastic volatility	$h_{t}=-0.20+0.95(h_{t-1}+0.20)+0.20\eta_{t}$ , $y_{t}=0.50y_{t-1}+\exp(h_{t}/2)\varepsilon_{t}$ .

Table 2: Synthetic data-generating processes. Innovations are Gaussian unless otherwise stated.

DGP	90% cov.	95% cov.	90% width/oracle	CRPS/oracle
Gaussian AR(1)	0.868	0.922	0.999	1.098
Gaussian random walk	0.877	0.933	1.284	1.196
Local trend	0.865	0.917	1.659	1.461
Threshold AR	0.845	0.908	1.002	1.100
Markov switching	0.861	0.900	1.098	1.287
Stochastic volatility	0.864	0.921	1.004	1.081

Table 3: Rollcast calibration and probabilistic efficiency relative to the true-DGP oracle, averaged over horizons one through six. CRPS/oracle and width/oracle equal one at oracle performance.

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Report the Floor: A Training-Free Conformal Interval Is a Mandatory Baseline for Probabilistic Time-Series Forecasting

Valery Manokhin

Independent researcher.

Time Series Forecasting Forecasting Benchmarks Conformal Prediction Probabilistic Time Series Forecasting Regression Prediction Intervals

Open paper AskPDF arXiv

Probabilistic forecasters are increasingly learned, yet the baselines they are compared against are often weak or omitted. We show that the simplest possible conformal interval - a last-value point forecast wrapped in a finite-sample split-conformal residual quantile, with no parameters and no training - is a far stronger baseline than its near-total absence from recent learned-forecasting and conformal-time-series comparisons would suggest. In one-step-ahead online forecasting across 2,217 real series from nine public sources (Monash, LOTSA, the LTSF traffic/electricity/weather suites, METR-LA, BOOM, nips/probts), this ConformalNaive interval decisively beats the naive value-quantile baselines, the entire NPTS family (NPTS 73%, SeasonalNPTS 64% of series), and the published Conformal Seasonal Pools (CSP) method (71% of series, bootstrap 95% CI [69,73], paired Wilcoxon p approx 7.6e-135); it is on par with the simpler learned conformal predictors (RCI, quantile regression; median relative Winkler within 2%) and is beaten only by the adaptive-online and ensemble methods (SPCI, ACI, AgACI), which track distribution shift and lead by 9-33% relative Winkler. It is also better calibrated than a trained neural forecaster: on the six datasets that introduced DeepNPTS, the trivial floors cover the truth 84-85% of the time at a nominal 95%, versus DeepNPTS's 66%. At multi-step seasonal horizons the picture inverts: the random-walk floor is the weakest method and the seasonal pool (CSP) wins - a boundary we map. Finally we give ConformalNaive+, a one-line, training-free, horizon-adaptive selector that attains the better of two complementary floors at every horizon with restored coverage. We argue the matching conformal naive floor must be a mandatory baseline whenever a learned probabilistic forecaster claims gains.

Abstract

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