Interweaving Marginals into Multivariate Sample Paths: Training-Free Dependence Construction for Probabilistic Time Series Foundation Models

Abstract:Probabilistic time series foundation models (TSFMs) provide coordinate-wise predictive distributions, but these marginals do not determine a joint distribution over multivariate future trajectories. We study training-free coupling of frozen TSFM marginals into multivariate forecast sample paths. Our primary evaluation fixes the empirical marginal sample multiset at every channel--horizon coordinate across methods, isolating the effect of coupling alone. Historical temporal and channel relations substantially improve their corresponding dependence diagnostics. The same pattern persists when the fixed-marginal constraint is removed and paths are sampled directly, and remains present under native multivariate backbone inference. These results support treating dependence reconstruction as a distinct post-processing problem for probabilistic TSFMs.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2609.25980 [cs.LG]

(or arXiv:2609.25980v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.25980 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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