Probabilistic Multivariate Time Series Forecasting with Diffusion Copulas
For financial risk managers, this work provides a method to accurately capture tail dependencies and systemic risk during extreme market events, addressing a critical bottleneck in current forecasting models.
The paper tackles the problem of multivariate time series forecasting for financial risk assessment, where existing diffusion models suffer from a 'normality bias' that underestimates tail risk. The proposed Diffusion-Copula framework decouples marginal and dependence learning, achieving superior performance over state-of-the-art baselines in forecasting systemic extremes in cryptocurrency markets, transforming 'Black Swan' events into 'Expected Crashes'.
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.