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Article

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

1
Department of Economics, Yildiz Technical University, 34220 Istanbul, Turkey
2
Department of Mathematical Engineering, Yildiz Technical University, 34220 Istanbul, Turkey
*
Author to whom correspondence should be addressed.
Academic Editor: Theodore E. Simos
Mathematics 2021, 9(14), 1708; https://doi.org/10.3390/math9141708
Received: 2 May 2021 / Revised: 10 July 2021 / Accepted: 11 July 2021 / Published: 20 July 2021
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
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 S2 manifolds that we consider, including the reference ones, employ matrix representations rather than differential operator representations of Lie algebras. Firstly, the performance of LieNLS 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 S2 manifold, namely Lie-LSTMOLS and Lie-LSTMNLS, are compared with those of the reference LieOLS and LieNLS models. The in-sample and out-of-sample results show that our proposed methods can achieve improved performance over LieOLS and LieNLS models in terms of RMSE and MAE metrics and hence can be more reliably used to assess volatility of time-series data. View Full-Text
Keywords: oil price forecasting; Lie group SO(3); LSTM; deep learning; short-term model oil price forecasting; Lie group SO(3); LSTM; deep learning; short-term model
MDPI and ACS Style

Bildirici, M.; Bayazit, N.G.; Ucan, Y. Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks. Mathematics 2021, 9, 1708. https://doi.org/10.3390/math9141708

AMA Style

Bildirici M, Bayazit NG, Ucan Y. Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks. Mathematics. 2021; 9(14):1708. https://doi.org/10.3390/math9141708

Chicago/Turabian Style

Bildirici, Melike, Nilgun G. Bayazit, and Yasemen Ucan. 2021. "Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks" Mathematics 9, no. 14: 1708. https://doi.org/10.3390/math9141708

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