Long-memory Time Series Generation with Neural Fractional SDE-Net

Abstract

In this research, we propose a novel method for generating time-series data using a neural network. Time-series data, especially data in real financial markets such as stock prices, is often sampled irregularly, and its noise structure is more complex than the standard Brownian motion. In order to generate time-series data with such characteristics, we extend and generalize the Neural Stochastic Differential Equation (SDE) model based on Brownian motion and propose Neural Fractional SDE-Net based on fractional Brownian motion. More specifically, we propose here the Neural Fractional SDE-Net (fSDE-Net) based on fractional Brownian motion whose the Hurst index is larger than half, which shows the long-term memory characteristics. We theoretically establish a numerical analysis method for fSDE-Net and show the existence and uniqueness of the solution for fSDE-Net. Furthermore, our experiments with various time series dataset demonstrate that the fSDE-Net model can replicate the long-term memory property well.