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

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  • Kohei Hayashi
  • Kei Nakagawa

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.

Suggested Citation

  • Kohei Hayashi & Kei Nakagawa, 2022. "Fractional SDE-Net: Generation of Time Series Data with Long-term Memory," Papers 2201.05974, arXiv.org, revised Aug 2022.
    • Handle: RePEc:arx:papers:2201.05974
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    References listed on IDEAS

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    6. Greene, Myron T. & Fielitz, Bruce D., 1977. "Long-term dependence in common stock returns," Journal of Financial Economics, Elsevier, vol. 4(3), pages 339-349, May.
    7. Benoit B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290, National Bureau of Economic Research, Inc.
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    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. Long-Memory Neural Nets
      by Francis Diebold in No Hesitations on 2022-02-28 12:12:00

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    1. Masanori Hirano & Kentaro Minami & Kentaro Imajo, 2023. "Adversarial Deep Hedging: Learning to Hedge without Price Process Modeling," Papers 2307.13217, arXiv.org.

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