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Adaptive Online Learning for the Autoregressive Integrated Moving Average Models

Author

Listed:
  • Weijia Shao

    (Faculty of Electrical Engineering and Computer Science, Technische Universität Berlin, Ernst-Reuter-Platz 7, 10587 Berlin, Germany)

  • Lukas Friedemann Radke

    (Faculty of Electrical Engineering and Computer Science, Technische Universität Berlin, Ernst-Reuter-Platz 7, 10587 Berlin, Germany)

  • Fikret Sivrikaya

    (GT-ARC Gemeinnützige GmbH, Ernst-Reuter-Platz 7, 10587 Berlin, Germany)

  • Sahin Albayrak

    (Faculty of Electrical Engineering and Computer Science, Technische Universität Berlin, Ernst-Reuter-Platz 7, 10587 Berlin, Germany
    GT-ARC Gemeinnützige GmbH, Ernst-Reuter-Platz 7, 10587 Berlin, Germany)

Abstract

This paper addresses the problem of predicting time series data using the autoregressive integrated moving average (ARIMA) model in an online manner. Existing algorithms require model selection, which is time consuming and unsuitable for the setting of online learning. Using adaptive online learning techniques, we develop algorithms for fitting ARIMA models without hyperparameters. The regret analysis and experiments on both synthetic and real-world datasets show that the performance of the proposed algorithms can be guaranteed in both theory and practice.

Suggested Citation

  • Weijia Shao & Lukas Friedemann Radke & Fikret Sivrikaya & Sahin Albayrak, 2021. "Adaptive Online Learning for the Autoregressive Integrated Moving Average Models," Mathematics, MDPI, vol. 9(13), pages 1-30, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1523-:d:584709
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    References listed on IDEAS

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    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Zhu Bangzhu & Julien Chevallier, 2017. "Pricing and Forecasting Carbon Markets: Models and Empirical Analyses," Post-Print hal-02879366, HAL.
    4. Tutun, Salih & Chou, Chun-An & Canıyılmaz, Erdal, 2015. "A new forecasting framework for volatile behavior in net electricity consumption: A case study in Turkey," Energy, Elsevier, vol. 93(P2), pages 2406-2422.
    5. Rounaghi, Mohammad Mahdi & Nassir Zadeh, Farzaneh, 2016. "Investigation of market efficiency and Financial Stability between S&P 500 and London Stock Exchange: Monthly and yearly Forecasting of Time Series Stock Returns using ARMA model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 10-21.
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