Valid and Expressive Copulas for Irregular Multivariate Time Series

Christian Klötergens; Tom Hanika; Lars Schmidt-Thieme; Vijaya Krishna Yalavarthi

cs.LGMay 22, 2026

Valid and Expressive Copulas for Irregular Multivariate Time Series

Authors: Christian Klötergens, Tom Hanika, Lars Schmidt-Thieme, Vijaya Krishna Yalavarthi

Abstract

We introduce CopFITi, a copula model for probabilistic forecasting of irregular multivariate time series (IMTS). Our model combines the expressivity of normalizing flows for univariate marginals with the consistency and flexibility of a Gaussian Mixture Copula for the joint dependency structure. Our experiments show that copula-based approaches, which decouple the marginals from the joint, yield better marginal models than architectures that directly fit the full joint. With CopFITi, we propose the first IMTS copula that is marginalization-consistent by construction and establish a new state of the art in joint IMTS density modeling.

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Apr 30, 2026 · cs.LGJ/K move · Enter open · S save

Probabilistic Circuits for Irregular Multivariate Time Series Forecasting

Christian Klötergens, Vijaya Krishna Yalavarthi, Lars Schmidt-Thieme

1ISMLL, University of Hildesheim, Germany

Joint probabilistic modeling is essential for forecasting irregular multivariate time series (IMTS) to accurately quantify uncertainty. Existing approaches often struggle to balance model expressivity with consistent marginalization, frequently leading to unreliable or contradictory forecasts. To address this, we propose CircuITS, a novel architecture for probabilistic IMTS forecasting based on probabilistic circuits. Our model is flexible in capturing intricate dependencies between time series channels while structurally guaranteeing valid joint distributions. Experiments on four real world datasets demonstrate that CircuITS achieves superior joint and marginal density estimation compared to state of the art baselines.

Multivariate Time Series Forecasting Time Series Circuits

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Abstract

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