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

2022Journal article Open access
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dc.contributor.authorBildirici, Melike
dc.contributor.authorUcan, Yasemen
dc.contributor.authorLousada, Sérgio
dc.date.accessioned2023-11-30T15:40:25Z
dc.date.available2023-11-30T15:40:25Z
dc.date.issued2022
dc.description.abstractThis 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, LieNLS, LieOLS, and LieGMM, respectively). Therefore, the interest rates that possess nonlinear structures and/or chaotic behaviors or outliers were tested with LieNLS, LieOLS, and LieGMM. We compared our LieNLS, LieOLS, and LieGMM results with the traditional OLS, NLS, and GMM methods, and the results favor the improvement achieved by the proposed LieNLS, LieOLS, and LieGMM 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.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationBildirici, M.; Ucan, Y.; Lousada, S. Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos. Mathematics 2022, 10, 3998. https://doi.org/10.3390/ math10213998pt_PT
dc.identifier.doi10.3390/math10213998pt_PT
dc.identifier.urihttp://hdl.handle.net/10400.13/5406
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherMDPIpt_PT
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/pt_PT
dc.subjectInterest ratept_PT
dc.subjectLie groupspt_PT
dc.subjectLie algebraspt_PT
dc.subjectStochastic differential equationpt_PT
dc.subjectOLSpt_PT
dc.subjectNLSpt_PT
dc.subjectGMMpt_PT
dc.subjectLieNLSpt_PT
dc.subjectLieOLSpt_PT
dc.subjectLieGMMpt_PT
dc.subject.pt_PT
dc.subjectFaculdade de Ciências Exatas e da Engenhariapt_PT
dc.titleInterest Rate Based on The Lie Group SO(3) in the Evidence of Chaospt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.issue21pt_PT
oaire.citation.startPage3998pt_PT
oaire.citation.titleMathematicspt_PT
oaire.citation.volume10pt_PT
person.familyNameBildirici
person.givenNameMelike
person.identifier.ciencia-idB31C-22D6-303E
person.identifier.orcid0000-0003-3925-844X
person.identifier.orcid0000-0002-8429-2164
person.identifier.scopus-author-id25631769500
rcaap.rightsopenAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication708b79c0-6553-4114-9a64-f599071d45df
relation.isAuthorOfPublication54151f72-c466-439b-b2cc-c539b2f8d477
relation.isAuthorOfPublication.latestForDiscovery708b79c0-6553-4114-9a64-f599071d45df

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