TEMPER: Temporal Encoder-Masked Probabilistic Ensemble Regressor for Time-Series Forecasting
Giancarlo Vercellino
Abstract
Probabilistic forecasting requires accurate central predictions and
calibrated uncertainty estimates. This paper presents TEMPER, the
Temporal Encoder-Masked Probabilistic Ensemble Regressor, a univariate
time-series forecasting algorithm that combines a temporal
autoencoder, a differentiable masked neural decision forest, continuous
ranked probability score (CRPS) training, and Gaussian-mixture
post-processing. The R implementation is built on torch for R and
returns horizon-wise density, distribution, quantile, and sampler functions.
We evaluate TEMPER on three deterministic synthetic level
series with trend, periodic, regime-switching, nonlinear-threshold, and
heteroskedastic components. Across 96 rolling-origin forecasts at horizons
t + 1, t + 5, t + 20, and t + 60, TEMPER obtains 2.824% mean
CRPS normalized by origin level, 3.635% median absolute error, and
68.8% empirical 90% interval coverage after training with a 300-epoch
cap and early-stopping patience of 100. A naive persistence bootstrap
has the best aggregate CRPS, 2.763%, while TEMPER has the best
median absolute error and the best CRPS at t+1 and t+5. The ablation
study uses matched series-origin-horizon cells, horizon-wise CRPS
deltas, endpoint sensitivity summaries, and a calibration-specific interval
study. Relaxing the learned mask improves average CRPS by 0.472
percentage points on the ablation subset, mainly through long-horizon
gains. A twofold interval inflation improves held-out coverage from
54.2% to 91.7% and gives the best 90% interval score among tested
calibration rules. The results identify calibration, horizon-specific tuning,
and component selection as the central research priorities.