论文标题
分数SDE网络：具有长期记忆的时间序列数据的生成
Fractional SDE-Net: Generation of Time Series Data with Long-term Memory
论文作者
论文摘要
在本文中，我们专注于使用神经网络的时间序列数据的生成。通常情况下，输入时间序列数据仅实现了一个（通常是不规则采样）路径，这使得很难提取时间序列特征，并且其噪声结构比I.I.D更为复杂。类型。时间序列数据，尤其是从水文，电信，经济学和金融的数据，也表现出长期记忆也称为长期依赖性（LRD）。本文的主要目的是在神经网络的帮助下人为地生成时间序列，从而考虑到路径的LRD。我们提出了FSDE-NET：神经分数随机微分方程网络。它通过使用大于一半的HURST指数的分数Brownian运动来概括神经随机微分方程模型，该方程式大于一半。我们得出FSDE-NET的求解器，并理论上分析了FSDE-NET解决方案的存在和唯一性。我们对人工和实时序列数据进行的实验表明，FSDE-NET模型可以很好地复制分布性能。
In this paper, we focus on the generation of time-series data using neural networks. It is often the case that input time-series data have only one realized (and usually irregularly sampled) path, which makes it difficult to extract time-series characteristics, and its noise structure is more complicated than i.i.d. type. Time series data, especially from hydrology, telecommunications, economics, and finance, exhibit long-term memory also called long-range dependency (LRD). The main purpose of this paper is to artificially generate time series with the help of neural networks, making the LRD of paths into account. We propose fSDE-Net: neural fractional Stochastic Differential Equation Network. It generalizes the neural stochastic differential equation model by using fractional Brownian motion with a Hurst index larger than half, which exhibits the LRD property. We derive the solver of fSDE-Net and theoretically analyze the existence and uniqueness of the solution to fSDE-Net. Our experiments with artificial and real time-series data demonstrate that the fSDE-Net model can replicate distributional properties well.
