CAST: Causal Anchored Simplex Transport for Distribution-Valued Time Series
Introduces CAST, a successor-local operator for forecasting distribution-valued time series that retrieves empirical successors from causal context, anchors them to persistence, and applies bounded local transport on the probability simplex.
CAST studies causal forecasting for distribution-valued time series, where each state is a probability vector on the simplex, such as queue occupancies, mobility shares, public-health mixtures, and energy compositions. CAST retrieves empirical successors from causal context, stabilizes them with a persistence anchor, and applies bounded local stochastic transport on ordered supports, preserving the simplex at every stage. The paper identifies latent transition-kernel aliasing, where similar observed distributions evolve differently under different regimes, and proves that forecasters relying on an aliased summary incur a weighted Jensen-Shannon excess-risk lower bound, while CAST can represent the regime-aware Bayes successor.