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Publication
Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos
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Advisor(s)
Abstract(s)
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, 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.
Description
Keywords
Interest rate Lie groups Lie algebras Stochastic differential equation OLS NLS GMM LieNLS LieOLS LieGMM . Faculdade de Ciências Exatas e da Engenharia
Citation
Bildirici, 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/ math10213998
Publisher
MDPI