Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of Chaos
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/3998 |
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| author | Melike Bildirici Yasemen Ucan Sérgio Lousada |
| author_facet | Melike Bildirici Yasemen Ucan Sérgio Lousada |
| author_sort | Melike Bildirici |
| collection | DOAJ |
| description | 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<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub>, respectively). Therefore, the interest rates that possess nonlinear structures and/or chaotic behaviors or outliers were tested with Lie<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub>. We compared our Lie<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub> results with the traditional OLS, NLS, and GMM methods, and the results favor the improvement achieved by the proposed Lie<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub> 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. |
| first_indexed | 2024-03-09T18:52:36Z |
| format | Article |
| id | doaj.art-22712253f0c74d008178797100c79a0f |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:52:36Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-22712253f0c74d008178797100c79a0f2023-11-24T05:43:19ZengMDPI AGMathematics2227-73902022-10-011021399810.3390/math10213998Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of ChaosMelike Bildirici0Yasemen Ucan1Sérgio Lousada2Faculty of Economics and Administrative Studies, Davutpaşa Campus, Yıldız Technical University, Esenler, İstanbul 34220, TurkeyMathematics Engineering, Davutpaşa Campus, Yıldız Technical University, Esenler, İstanbul 34220, TurkeyDepartment of Civil Engineering and Geology (DECG), Faculty of Exact Sciences and Engineering (FCEE), University of Madeira (UMa), 9000-082 Funchal, PortugalThis 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<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub>, respectively). Therefore, the interest rates that possess nonlinear structures and/or chaotic behaviors or outliers were tested with Lie<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub>. We compared our Lie<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub> results with the traditional OLS, NLS, and GMM methods, and the results favor the improvement achieved by the proposed Lie<sub>NLS</sub>, Lie<sub>OLS</sub>, and Lie<sub>GMM</sub> 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.https://www.mdpi.com/2227-7390/10/21/3998interest rateLie groupsLie algebrasstochastic differential equationOLSNLS |
| spellingShingle | Melike Bildirici Yasemen Ucan Sérgio Lousada Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of Chaos Mathematics interest rate Lie groups Lie algebras stochastic differential equation OLS NLS |
| title | Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of Chaos |
| title_full | Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of Chaos |
| title_fullStr | Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of Chaos |
| title_full_unstemmed | Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of Chaos |
| title_short | Interest Rate Based on The Lie Group <i>SO(3)</i> in the Evidence of Chaos |
| title_sort | interest rate based on the lie group i so 3 i in the evidence of chaos |
| topic | interest rate Lie groups Lie algebras stochastic differential equation OLS NLS |
| url | https://www.mdpi.com/2227-7390/10/21/3998 |
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