TEMPER: Temporal Encoder-Masked Probabilistic Ensemble Regressor for Time-Series Forecasting

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.