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Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks

Author

Listed:
  • Melike Bildirici

    (Department of Economics, Yildiz Technical University, 34220 Istanbul, Turkey)

  • Nilgun Guler Bayazit

    (Department of Mathematical Engineering, Yildiz Technical University, 34220 Istanbul, Turkey)

  • Yasemen Ucan

    (Department of Mathematical Engineering, Yildiz Technical University, 34220 Istanbul, Turkey)

Abstract

In this paper, we propose hybrid models for modelling the daily oil price during the period from 2 January 1986 to 5 April 2021. The models on S 2 manifolds that we consider, including the reference ones, employ matrix representations rather than differential operator representations of Lie algebras. Firstly, the performance of Lie NLS model is examined in comparison to the Lie-OLS model. Then, both of these reference models are improved by integrating them with a recurrent neural network model used in deep learning. Thirdly, the forecasting performance of these two proposed hybrid models on the S 2 manifold, namely Lie-LSTM OLS and Lie-LSTM NLS , are compared with those of the reference Lie OLS and Lie NLS models. The in-sample and out-of-sample results show that our proposed methods can achieve improved performance over Lie OLS and Lie NLS models in terms of RMSE and MAE metrics and hence can be more reliably used to assess volatility of time-series data.

Suggested Citation

  • Melike Bildirici & Nilgun Guler Bayazit & Yasemen Ucan, 2021. "Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks," Mathematics, MDPI, vol. 9(14), pages 1-10, July.
  • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1708-:d:597836
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    References listed on IDEAS

    as
    1. Melike Bildirici & Nilgun Guler Bayazit & Yasemen Ucan, 2020. "Analyzing Crude Oil Prices under the Impact of COVID-19 by Using LSTARGARCHLSTM," Energies, MDPI, vol. 13(11), pages 1-18, June.
    2. C. F. Lo & C. H. Hui, 2001. "Valuation of financial derivatives with time-dependent parameters: Lie-algebraic approach," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 73-78.
    3. Akbar Komijani & Esmaeil Naderi & Nadiya Gandali Alikhani, 2014. "A hybrid approach for forecasting of oil prices volatility," OPEC Energy Review, Organization of the Petroleum Exporting Countries, vol. 38(3), pages 323-340, September.
    4. Gibson, Rajna & Schwartz, Eduardo S, 1990. "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-976, July.
    5. Lahmiri, Salim, 2017. "A study on chaos in crude oil markets before and after 2008 international financial crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 389-395.
    6. Adrangi, Bahram & Chatrath, Arjun & Dhanda, Kanwalroop Kathy & Raffiee, Kambiz, 2001. "Chaos in oil prices? Evidence from futures markets," Energy Economics, Elsevier, vol. 23(4), pages 405-425, July.
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    Cited by:

    1. Melike Bildirici & Yasemen Ucan & Sérgio Lousada, 2022. "Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos," Mathematics, MDPI, vol. 10(21), pages 1-9, October.

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