用深度神经网络高效精准估计时间序列长记忆参数。
Parameter Estimation of Long Memory Stochastic Processes with Deep Neural Networks
- 基于生成器合成数据，训练可缩放的1D CNN与LSTM模型
- 在fBm、ARFIMA、fOU上均超越传统统计方法
- 适合金融、物理等领域需要快速参数估计的研究者
我们提出一种完全基于深度神经网络的方法，用于估计包含长程依赖现象的时间序列模型中的长记忆参数。如赫斯特指数等参数对于刻画随机过程的长程依赖性、粗糙性和自相似性至关重要。这些参数的准确快速估计在金融、物理和工程等多个科学领域具有重要意义。我们利用高效的流程生成器提供高质量的合成训练数据，训练出具备尺度不变性的1D卷积神经网络（CNN）和长短期记忆（LSTM）模型。实验表明，我们的神经模型在分数布朗运动（fBm）、自回归分数积分移动平均（ARFIMA）过程和分数奥恩斯坦-乌伦贝克（fOU）过程中，均显著优于传统统计方法，甚至优于那些已引入神经网络的改进方法。其精度、速度、一致性和鲁棒性得到充分验证。我们相信本工作将推动深度学习在随机过程建模与参数估计领域的进一步研究。
原文摘要 · Abstract (English)
We present a purely deep neural network-based approach for estimating long memory parameters of time series models that incorporate the phenomenon of long-range dependence. Parameters, such as the Hurst exponent, are critical in characterizing the long-range dependence, roughness, and self-similarity of stochastic processes. The accurate and fast estimation of these parameters holds significant importance across various scientific disciplines, including finance, physics, and engineering. We harnessed efficient process generators to provide high-quality synthetic training data, enabling the training of scale-invariant 1D Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) models. Our neural models outperform conventional statistical methods, even those augmented with neural networks. The precision, speed, consistency, and robustness of our estimators are demonstrated through experiments involving fractional Brownian motion (fBm), the Autoregressive Fractionally Integrated Moving Average (ARFIMA) process, and the fractional Ornstein-Uhlenbeck (fOU) process. We believe that our work will inspire further research in the field of stochastic process modeling and parameter estimation using deep learning techniques.
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