SBBTS统一生成金融时间序列，同时还原波动率与趋势。
SBBTS: A Unified Schrödinger-Bass Framework for Synthetic Financial Time Series
- 基于薛定谔-巴斯桥框架，联合建模时间序列的漂移与随机波动。
- 在赫斯顿模型上准确恢复波动率和相关性参数，优于传统方法。
- 用于标普500数据增强后，预测性能显著提升，适合量化金融应用。
我们研究生成同时保留边缘分布与时间动态的合成时间序列问题，这是金融机器学习中的核心挑战。现有方法通常无法联合建模漂移与随机波动：基于扩散的方法固定波动率，而鞅传输模型忽略漂移。本文提出时间序列的薛定谔-巴斯桥（SBBTS），将薛定谔-巴斯公式扩展至多步时间序列。该方法构建一个联合校准漂移与波动率的扩散过程，并可分解为可处理的条件传输问题，实现高效学习。数值实验表明，SBBTS在赫斯顿模型上能准确恢复随机波动率和相关性参数，而以往的薛定谔桥方法未能捕捉。应用于标普500数据时，使用SBBTS生成的合成序列进行数据增强，下游预测性能持续提升，分类准确率与夏普比率均高于仅用真实数据训练的结果。结果表明，SBBTS为金融应用中的真实时间序列生成与数据增强提供了一种实用有效的框架。
原文摘要 · Abstract (English)
We study the problem of generating synthetic time series that reproduce both marginal distributions and temporal dynamics, a central challenge in financial machine learning. Existing approaches typically fail to jointly model drift and stochastic volatility, as diffusion-based methods fix the volatility while martingale transport models ignore drift. We introduce the Schrödinger-Bass Bridge for Time Series (SBBTS), a unified framework that extends the Schrödinger-Bass formulation to multi-step time series. The method constructs a diffusion process that jointly calibrates drift and volatility and admits a tractable decomposition into conditional transport problems, enabling efficient learning. Numerical experiments on the Heston model demonstrate that SBBTS accurately recovers stochastic volatility and correlation parameters that prior SchrödingerBridge methods fail to capture. Applied to S&P 500 data, SBBTS-generated synthetic time series consistently improve downstream forecasting performance when used for data augmentation, yielding higher classification accuracy and Sharpe ratio compared to real-data-only training. These results show that SBBTS provides a practical and effective framework for realistic time series generation and data augmentation in financial applications.
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