用深度模型直接预测金融收益分布，效果媲美经典方法。
Forecasting Probability Distributions of Financial Returns with Deep Neural Networks
- 用CNN和LSTM直接学习正态、t分布等参数
- LSTM+偏斜t分布模型在多指标中表现最佳
- 适合金融风险与投资组合管理研究者
本研究评估了深度神经网络在预测金融收益概率分布上的表现。采用一维卷积神经网络（CNN）和长短期记忆网络（LSTM）对正态分布、学生t分布及偏斜学生t分布的参数进行建模，并使用自定义负对数似然损失函数直接优化分布参数。模型在六个主要股票指数（标普500、巴西博韦斯帕、德国DAX、波兰WIG、日经225、韩国KOSPI）上进行测试，采用对数预测得分（LPS）、连续排名概率评分（CRPS）和概率积分变换（PIT）等概率评价指标。结果表明，深度学习模型能提供精确的分布预测，在价值风险（VaR）估计方面与传统GARCH模型表现相当。其中，LSTM搭配偏斜学生t分布的模型在多个评估标准下表现最优，能够有效捕捉金融收益的厚尾性和非对称性。研究证明，深度神经网络是金融风险评估与组合管理中传统计量模型的可行替代方案。
原文摘要 · Abstract (English)
This study evaluates deep neural networks for forecasting probability distributions of financial returns. 1D convolutional neural networks (CNN) and Long Short-Term Memory (LSTM) architectures are used to forecast parameters of three probability distributions: Normal, Student's t, and skewed Student's t. Using custom negative log-likelihood loss functions, distribution parameters are optimized directly. The models are tested on six major equity indices (S\&P 500, BOVESPA, DAX, WIG, Nikkei 225, and KOSPI) using probabilistic evaluation metrics including Log Predictive Score (LPS), Continuous Ranked Probability Score (CRPS), and Probability Integral Transform (PIT). Results show that deep learning models provide accurate distributional forecasts and perform competitively with classical GARCH models for Value-at-Risk estimation. The LSTM with skewed Student's t distribution performs best across multiple evaluation criteria, capturing both heavy tails and asymmetry in financial returns. This work shows that deep neural networks are viable alternatives to traditional econometric models for financial risk assessment and portfolio management.
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