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

TL;DR

This paper introduces fSDE-Net, a neural network model that generates time series data with long-term memory by incorporating fractional Brownian motion, addressing challenges in modeling complex, irregularly sampled real-world data.

Contribution

The paper proposes a novel neural fractional SDE model that captures long-range dependency in time series, extending neural SDEs with fractional Brownian motion.

Findings

fSDE-Net effectively replicates distributional properties of real data.

Theoretical analysis confirms existence and uniqueness of solutions.

Model captures long-term memory in generated time series.

Abstract

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.