Diffolio: A Diffusion Model for Multivariate Probabilistic Financial Time-Series Forecasting and Portfolio Construction

Probabilistic forecasting is crucial in multivariate financial time-series for constructing efficient portfolios that account for complex cross-sectional dependencies. In this paper, we propose Diffolio, a diffusion model designed for multivariate financial time-series forecasting and portfolio construction. Diffolio employs a denoising network with a hierarchical attention architecture, comprising both asset-level and market-level layers. Furthermore, to better reflect cross-sectional correlations, we introduce a correlation-guided regularizer informed by a stable estimate of the target correlation matrix. This structure effectively extracts salient features not only from historical returns but also from asset-specific and systematic covariates, significantly enhancing the performance of forecasts and portfolios. Experimental results on the daily excess returns of 12 industry portfolios show that Diffolio outperforms various probabilistic forecasting baselines in multivariate forecasting accuracy and portfolio performance. Moreover, in portfolio experiments, portfolios constructed from Diffolio's forecasts show consistently robust performance, thereby outperforming those from benchmarks by achieving higher Sharpe ratios for the mean-variance tangency portfolio and higher certainty equivalents for the growth-optimal portfolio. These results demonstrate the superiority of our proposed Diffolio in terms of not only statistical accuracy but also economic significance.

Forecasting VIX using interpretable Kolmogorov-Arnold networks

This paper presents the use of Kolmogorov-Arnold Networks (KANs) for forecasting the CBOE Volatility Index (VIX). Unlike traditional MLP-based neural networks that are often criticized for their black-box nature, KAN offers an interpretable approach via learnable spline-based activation functions and symbolification. Based on a parsimonious architecture with symbolic functions, KAN expresses a forecast of the VIX as a closed-form in terms of explanatory variables, and provide interpretable insights into key characteristics of the VIX, including mean reversion and the leverage effect. Through in-depth empirical analysis across multiple datasets and periods, we show that KANs achieve competitive forecasting performance while requiring significantly fewer parameters compared to MLP-based neural network models. Our findings demonstrate the capacity and potential of KAN as an interpretable financial time-series forecasting method.

Denoising Task Difficulty-based Curriculum for Training Diffusion Models

Diffusion-based generative models have emerged as powerful tools in the realm of generative modeling. Despite extensive research on denoising across various timesteps and noise levels, a conflict persists regarding the relative difficulties of the denoising tasks. While various studies argue that lower timesteps present more challenging tasks, others contend that higher timesteps are more difficult. To address this conflict, our study undertakes a comprehensive examination of task difficulties, focusing on convergence behavior and changes in relative entropy between consecutive probability distributions across timesteps. Our observational study reveals that denoising at earlier timesteps poses challenges characterized by slower convergence and higher relative entropy, indicating increased task difficulty at these lower timesteps. Building on these observations, we introduce an easy-to-hard learning scheme, drawing from curriculum learning, to enhance the training process of diffusion models. By organizing timesteps or noise levels into clusters and training models with descending orders of difficulty, we facilitate an order-aware training regime, progressing from easier to harder denoising tasks, thereby deviating from the conventional approach of training diffusion models simultaneously across all timesteps. Our approach leads to improved performance and faster convergence by leveraging the benefits of curriculum learning, while maintaining orthogonality with existing improvements in diffusion training techniques. We validate these advantages through comprehensive experiments in image generation tasks, including unconditional, class-conditional, and text-to-image generation.