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Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos

Author

Listed:
  • Melike Bildirici

    (Faculty of Economics and Administrative Studies, Davutpaşa Campus, Yıldız Technical University, Esenler, İstanbul 34220, Turkey)

  • Yasemen Ucan

    (Mathematics Engineering, Davutpaşa Campus, Yıldız Technical University, Esenler, İstanbul 34220, Turkey)

  • Sérgio Lousada

    (Department of Civil Engineering and Geology (DECG), Faculty of Exact Sciences and Engineering (FCEE), University of Madeira (UMa), 9000-082 Funchal, Portugal
    CITUR—Madeira—Research Centre for Tourism Development and Innovation, 9000-082 Funchal, Portugal
    VALORIZA—Research Centre for Endogenous Resource Valorization, Polytechnic Institute of Portalegre (IPP), 7300 Portalegre, Portugal
    Environmental Resources Analysis Research Group (ARAM), University of Extremadura, 06071 Badajoz, Spain)

Abstract

This paper aims to test the structure of interest rates during the period from 1 September 1981 to 28 December 2020 by using Lie algebras and groups. The selected period experienced substantial events impacting interest rates, such as the economic crisis, the military intervention of the USA in Iraq, and the COVID-19 pandemic, in which economies were in lockdown. These conditions caused the interest rate to have a nonlinear structure, chaotic behavior, and outliers. Under these conditions, an alternative method is proposed to test the random and nonlinear structure of interest rates to be evolved by a stochastic differential equation captured on a curved state space based on Lie algebras and group. Then, parameter estimates of this equation were obtained by OLS, NLS, and GMM estimators (hereafter, Lie NLS , Lie OLS , and Lie GMM , respectively). Therefore, the interest rates that possess nonlinear structures and/or chaotic behaviors or outliers were tested with Lie NLS , Lie OLS , and Lie GMM . We compared our Lie NLS , Lie OLS , and Lie GMM results with the traditional OLS, NLS, and GMM methods, and the results favor the improvement achieved by the proposed Lie NLS , Lie OLS , and Lie GMM in terms of the RMSE and MAE in the out-of-sample forecasts. Lastly, the Lie algebras with NLS estimators exhibited the lowest RMSE and MAE followed by the Lie algebras with GMM, and the Lie algebras with OLS, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:3998-:d:955591
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    References listed on IDEAS

    as
    1. 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.
    2. Michelle Muniz & Matthias Ehrhardt & Michael Günther, 2021. "Approximating Correlation Matrices Using Stochastic Lie Group Methods," Mathematics, MDPI, vol. 9(1), pages 1-10, January.
    3. 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.
    4. Yusuke Morimoto & Makiko Sasada, 2017. "Algebraic structure of vector fields in financial diffusion models and its applications," Quantitative Finance, Taylor & Francis Journals, vol. 17(7), pages 1105-1117, July.
    5. Suren Basov, 2004. "Lie Groups of Partial Differential Equations and Their Application to theMultidimensional Screening Problems," Department of Economics - Working Papers Series 895, The University of Melbourne.
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