标题： 引入$σ$-单元：在基于RNN的波动率预测中统一GARCH、随机波动和演化机制 显示英文标题

标题： Introducing the $σ$-Cell: Unifying GARCH, Stochastic Fluctuations and Evolving Mechanisms in RNN-based Volatility Forecasting

摘要： 本文介绍了$\sigma$-Cell，一种用于金融波动率建模的新型循环神经网络（RNN）架构。 将传统的计量经济学方法如 GARCH 与深度学习相结合，$\sigma$-Cell 融入了随机层和时变参数以捕捉动态波动模式。 我们的模型作为一个生成网络，近似潜在变量的条件分布。 我们采用基于对数似然的损失函数和专用激活函数来提升性能。 实验结果表明，相比传统的 GARCH 和随机波动率模型，具有更优的预测准确性，标志着将领域知识与神经网络结合的下一步。 显示英文摘要

摘要： This paper introduces the $\sigma$-Cell, a novel Recurrent Neural Network (RNN) architecture for financial volatility modeling. Bridging traditional econometric approaches like GARCH with deep learning, the $\sigma$-Cell incorporates stochastic layers and time-varying parameters to capture dynamic volatility patterns. Our model serves as a generative network, approximating the conditional distribution of latent variables. We employ a log-likelihood-based loss function and a specialized activation function to enhance performance. Experimental results demonstrate superior forecasting accuracy compared to traditional GARCH and Stochastic Volatility models, making the next step in integrating domain knowledge with neural networks.