Valid and Expressive Copulas for Irregular Multivariate Time Series

2026-05-22

AI Summary

This work addresses the challenges of joint distribution modeling in probabilistic forecasting for irregular multivariate time series, where coupling between marginal distributions and dependency structures often introduces bias. To resolve this, we propose CopFITi, a novel model that decouples marginals from dependencies: it employs normalizing flows to flexibly model univariate marginal distributions and leverages a Gaussian mixture copula to capture complex multivariate dependencies. CopFITi is the first copula-based model for irregular multivariate time series that is explicitly constructed to satisfy marginal consistency by design. Experimental results demonstrate that CopFITi achieves state-of-the-art performance in joint density estimation, significantly improving both marginal calibration and overall predictive accuracy.

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.

Problem

• irregular multivariate time series
• copula
• probabilistic forecasting
• marginalization-consistency
• joint density modeling

Innovation

• Copula
• Irregular Multivariate Time Series
• Normalizing Flows
• Marginalization Consistency
• Probabilistic Forecasting