Fractional SDE-Net: Generation of Time Series Data with Long-term Memory

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.