Chirp-Modal Gaussian Mixtures for Joint Forecasting at Irregular Times

Probabilistic forecasting of irregular time series demands coherent uncertainty across future times. Accurate pointwise intervals alone may neglect the temporal dependence that governs plausible trajectories. We propose chirp-modal Gaussian mixtures, which integrate damped oscillations with an explicit temporal covariance. Within each component, frequency and decay dynamically shift within the forecast window, enabling both the mean and the alignment of uncertainty to adapt over time. A commuting dynamical structure affords analytic means and transitions, while positive variance integration enables efficient joint sampling at irregular queries. We generate these components directly from history (CMD-X) or via latent reverse diffusion (CMD-D), and learn their temporal covariance with full-grid likelihoods. On all tested datasets, direct chirp mixtures consistently reduce energy and variogram scores relative to fixed-pole mixtures at comparable trainable parameter counts. At the headline configuration, iterative generation further improves joint scores, and same-checkpoint comparisons validate keeping mixture structure beyond a single Gaussian. Our approach combines adaptable temporal dependence with a choice of direct or iterative generation.