Probabilistic Multivariate Time Series Forecasting with Diffusion Copulas

TL;DR

This paper introduces a Diffusion-Copula framework for multivariate time series forecasting that improves tail risk estimation and dependence modeling, especially during extreme market events.

Contribution

It decouples marginal distribution learning from dependence structure modeling using deep Mixture Density Networks and Classification-Diffusion Copulas, enhancing risk assessment.

Findings

Outperforms state-of-the-art baselines in forecasting systemic extremes.

Identifies 'Expected Crashes' as low surprise events, unlike baseline models.

Demonstrates superior tail risk capture in cryptocurrency markets.

Abstract

Accurately assessing financial risk requires capturing both individual asset volatility and the complex, asymmetric dependence structures that emerge during extreme market events. While modern diffusion-based models have advanced multivariate forecasting, they often suffer from a "normality bias" when trained end-to-end, sacrificing marginal calibration for joint coherence and consistently underestimating tail risk. To address this, we propose a Diffusion-Copula framework that explicitly decouples the learning of marginal distributions from their dependence structure. We employ deep Mixture Density Networks to capture heavy-tailed asset dynamics, followed by a Classification-Diffusion Copula to model the joint dependence. Applied to cryptocurrency markets, our approach demonstrates superior performance over state-of-the-art baselines in forecasting systemic extremes of both marginal and joint events. Crucially, we demonstrate that while baseline models classify simultaneous market crashes as statistically impossible "Black Swans" (high surprise), our framework identifies them as "Expected Crashes" (low surprise), successfully preserving the correlation structure necessary for robust risk management during contagion events.