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 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.
Highlights
Crude oil is a strategic natural resource since it is a commodity connected with many financial instruments, such as futures, options, and bonds
The Lie group SO(3) is a differential manifold, and it can be identified with unit sphere S2
We have proposed hybrid models for analyzing the short-term model of the oil during the period from 2 January 1986 to 5 April 2021
Summary
Crude oil is a strategic natural resource since it is a commodity connected with many financial instruments, such as futures, options, and bonds. The nonlinear behavior in the oil price has been well discussed and analyzed by many articles in the past. Barone-Adesi et al [1] suggested a semiparametric method to examine the structure of oil prices. Adrangi et al [2] determined the presence of low-dimensional chaotic structure in the oil prices. Lahmiri [3], Bildirici, and Sonustun [4]; Komijani et al [5]; and He [6] are the other studies that determine the presence of chaos in the oil prices. Bildirici et al [7] suggested a new hybrid modelling technique based on the LSTARGARCH and LSTM models to analyze the volatility of oil prices
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