Air temperature measurement based on lie group SO(3)

Ucan, Yasemen; Bildirici, Melike

doi:10.2298/tsci2204089u

Cited by 6 publications

(5 citation statements)

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“…Choose an initial set of parameters, B ∈ so(3). The covariance matrix for the Wiener process is assumed to be W. Generate a sufficient number of sample paths for the short rate, and determine the time series for all the spot rates; denote the estimated spot rate data by R(t, t + τ) (see [7,14,17] for similar app.). Determine if the choice of model parameters is an optimizer for the objective function:…”

Section: Data and Resultsmentioning

confidence: 99%

“…In the context of applied mathematics, the paper contributes by the simultaneous utilization of the Lie OLS , Lie NLS , and Lie GMM models to obtain parameter estimations. In the context of financial mathematics, Park et al [7], Goard [16], Bildirici et al [14], and Ucan and Bildirici [17] used only the OLS estimation method. This paper used three different methods: OLS, NLS, and GMM.…”

Section: Introductionmentioning

confidence: 99%

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

2022

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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.

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Section: Data and Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2022

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“…Meanwhile, [6] uncovered evidence of chaotic structures in NO, CO, SO 2 , PM10, and NO 2 with the utilization of the Lyapunov exponent. In addition, [7] detected chaotic characteristics in the air pollution index (API) in Lanzhou, northwest China; [8] explored chaotic dynamics of air pollution in India, China, and Türkiye; and [9] examined chaotic dynamics of air temperature with Lie group algebra. While these studies explored the factors affecting environmental pollution and the effects of metaverse and energy consumption, their chaotic structure with longterm dependence leading to nonlinearity in contagion and causal relations have not been explored in the literature.…”

Section: Introductionmentioning

confidence: 99%

Chaos, Fractionality, Nonlinear Contagion, and Causality Dynamics of the Metaverse, Energy Consumption, and Environmental Pollution: Markov-Switching Generalized Autoregressive Conditional Heteroskedasticity Copula and Causality Methods

Bildirici,

Ersin,

Ibrahim

2024

Fractal Fract

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Metaverse (MV) technology introduces new tools for users each day. MV companies have a significant share in the total stock markets today, and their size is increasing. However, MV technologies are questioned as to whether they contribute to environmental pollution with their increasing energy consumption (EC). This study explores complex nonlinear contagion with tail dependence and causality between MV stocks, EC, and environmental pollution proxied with carbon dioxide emissions (CO2) with a decade-long daily dataset covering 18 May 2012–16 March 2023. The Mandelbrot–Wallis and Lo’s rescaled range (R/S) tests confirm long-term dependence and fractionality, and the largest Lyapunov exponents, Shannon and Havrda, Charvât, and Tsallis (HCT) entropy tests followed by the Kolmogorov–Sinai (KS) complexity measure confirm chaos, entropy, and complexity. The Brock, Dechert, and Scheinkman (BDS) test of independence test confirms nonlinearity, and White‘s test of heteroskedasticity of nonlinear forms and Engle’s autoregressive conditional heteroskedasticity test confirm heteroskedasticity, in addition to fractionality and chaos. In modeling, the marginal distributions are modeled with Markov-Switching Generalized Autoregressive Conditional Heteroskedasticity Copula (MS-GARCH–Copula) processes with two regimes for low and high volatility and asymmetric tail dependence between MV, EC, and CO2 in all regimes. The findings indicate relatively higher contagion with larger copula parameters in high-volatility regimes. Nonlinear causality is modeled under regime-switching heteroskedasticity, and the results indicate unidirectional causality from MV to EC, from MV to CO2, and from EC to CO2, in addition to bidirectional causality among MV and EC, which amplifies the effects on air pollution. The findings of this paper offer vital insights into the MV, EC, and CO2 nexus under chaos, fractionality, and nonlinearity. Important policy recommendations are generated.

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“…On the quantum level, it allows a consistent description of the rotational spectra of molecules [5][6][7][8][9][10][11][12][13][14][15][16][17]. Moreover, using SO(3) as a configuration manifold leads to several applications including texture analysis [18][19][20], protein-protein docking [21,22], air tempertature control [23], structure of interest rates (in economics) [24], attitude of rigid body [25][26][27][28][29][30], quantum information [31] or spherical image analysis [32,33].…”

Section: Introductionmentioning

confidence: 99%

Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder

Gazeau,

Murenzi

2023

Preprint

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Covariant integral quantization with rotational symmetry SO(3) is established for the quantum motion on this group manifold, or, alternatively, for Gabor signal analysis on this group. We revisit the action of the related (non-unitary) Weyl-Gabor operator on the Hilbert space of square integrable functions on SO(3) and disclose a set of various properties. By selecting weight functions on the corresponding discrete-continuous phase space, one derives related coherent states and Wigner transform.

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Air temperature measurement based on lie group SO(3)

Cited by 6 publications

References 10 publications

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

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

Chaos, Fractionality, Nonlinear Contagion, and Causality Dynamics of the Metaverse, Energy Consumption, and Environmental Pollution: Markov-Switching Generalized Autoregressive Conditional Heteroskedasticity Copula and Causality Methods

Covariant Integral Quantization of the Semi-Discrete SO(3)-Hypercylinder

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