CADRE: Distributional Refinement for Probabilistic Time Series Forecasting

Existing probabilistic time series forecasters often map temporal observations to predictive distributions through predefined parametric heads, such as Student-$t$ and Gaussian. However, these distributional assumptions can limit their ability to capture asymmetric and irregular conditional distributions in real time series. To address this challenge, we introduce $\underline{CA}$libration via $\underline{D}$istributional $\underline{RE}$finement (CADRE), a framework that uses a base forecast to guide a more flexible predictive distribution. CADRE constructs input-adaptive bins from the forecaster’s predicted quantiles and uses a lightweight refinement head to learn each bin’s probability mass from shared temporal features. Experiments on six real world datasets demonstrate consistent improvements in probabilistic forecasting and gains in point forecast accuracy. Further experiments show that CADRE improves forecasting performance when transferring models across datasets. A channel-level analysis on Weather reveals an association between greater marginal skewness and larger probabilistic gains, suggesting that CADRE is particularly beneficial for forecasting asymmetric time series.