In this paper, we focus on generation of time-series data using neural networks. It is often the case that input time-series data, especially taken from real financial markets, is irregularly sampled, and its noise structure is more complicated than i.i.d. type. To generate time series with such a property, we propose fSDE-Net: neural fractional Stochastic Differential Equation Network. It generalizes the neural SDE model by using fractional Brownian motion with Hurst index larger than half, which exhibits long-term memory property. We derive the solver of fSDE-Net and theoretically analyze the existence and uniqueness of the solution to fSDE-Net. Our experiments demonstrate that the fSDE-Net model can replicate distributional properties well.
翻译:在本文中,我们的重点是利用神经网络生成时间序列数据。输入时间序列数据,特别是来自实际金融市场的数据,往往是不定期抽样的,而且其噪音结构比i.i.d.类型更加复杂。为了生成这种属性的时间序列,我们建议FSDE-Net:神经分数存储差异计算网络。它通过使用分数的Brownian运动和半重的Hurst指数来概括神经SDE模型,显示长期记忆属性。我们从FSDE-Net的求解器和理论上分析FSDE-Net解决方案的存在和独特性。我们的实验表明,FSDE-Net模型可以很好地复制分布特性。