ClockUp: Clock-Structured Additive Uncertainty Modeling for Non-stationary Probabilistic Time Series Forecasting

Reliable probabilistic time series forecasting requires adapting to local distribution shifts while capturing recurring temporal structure. Although instance normalization mitigates variation in local level and scale, similar normalized histories can occur at different cycle positions even when their future distributions differ. Consequently, latent uncertainty models conditioned solely on normalized history may struggle to distinguish phase-dependent predictive distributions, a limitation we term $\text{phase blindness}$. To address this limitation, we propose $\text{ClockUp}$, a $\text{Clock}$-structured framework that explicitly incorporates temporal phase into latent $\text{U}$ncertainty modeling and $\text{p}$robabilistic forecasting. ClockUp combines a history-conditioned Gaussian state component with a Fourier-phase-conditioned Gaussian clock component to form an additive latent prior, enabling direct reparameterized sampling with closed-form mean and variance. A push-forward decoder further combines lead-time-specific and phase-conditioned mappings to generate forecasts non-iteratively. We train ClockUp using empirical CRPS and additionally investigate P-CRPS, a phase-balanced training variant designed to reduce scale-driven loss imbalance across phases. Experiments on seven real-world benchmarks demonstrate improved probabilistic and point forecasting accuracy. Together with phase-wise analyses on selected datasets, these results support explicit phase conditioning as a useful inductive bias for probabilistic forecasting and highlight the value of phase-wise calibration diagnostics.