Lisandro Fermin

Faculty ,  Aix-Marseille Université , Faculté d'économie et de gestion (FEG)

Econometrics, Finance and mathematical methods
Fermin
Status
Assistant professor
Research domain(s)
Econometrics
Thesis
2008, Université Paris-Sud XI
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Contact
lisandro.fermin[at]univ-amu.fr
Address

Maison de l'économie et de la gestion d'Aix
424 chemin du viaduc, CS80429
13097 Aix-en-Provence Cedex 2

Abstract The Geographically and Temporally Weighted Regression (GTWR) model is a well-established local technique for analyzing spatial heterogeneity and temporal dependence in georeferenced data. It is recognized for its ability to represent real-world settings. In this study, we expand upon the GTWR model by incorporating spatio-temporal noise that is colored in space and fractional in time. Under this formulation, we derive the Weighted Least Squares (WLS) estimator and formally establish its convergence rate. To evaluate the performance of the WLS estimator, we implemented a simulation study with five defined scenarios. The simulation results indicate that the model residuals exhibit small variations around zero, which suggests the accuracy of the estimator. Finally, we applied the estimator to real data on the incidence of respiratory diseases. Analyzing the residuals in this empirical application allows us to evaluate the ability of the model to capture the spatio-temporal structure of the data.
Keywords Geographically and Temporally Weighted Regression, Fractional Colored Noise, Consistency
Publication HAL Google Scholar
Abstract The Geographically and Temporally Weighted Regression (GTWR) model is a well-established local technique for analyzing spatial heterogeneity and temporal dependence in georeferenced data. It is recognized for its ability to represent real-world settings. In this study, we expand upon the GTWR model by incorporating spatio-temporal noise that is colored in space and fractional in time. Under this formulation, we derive the Weighted Least Squares (WLS) estimator and formally establish its convergence rate. To evaluate the performance of the WLS estimator, we implemented a simulation study with five defined scenarios. The simulation results indicate that the model residuals exhibit small variations around zero, which suggests the accuracy of the estimator. Finally, we applied the estimator to real data on the incidence of respiratory diseases. Analyzing the residuals in this empirical application allows us to evaluate the ability of the model to capture the spatio-temporal structure of the data.
Keywords Consistency, Fractional Colored Noise, Geographically and Temporally Weighted Regression
Publication HAL Google Scholar
Abstract We study a stochastic functional differential equation (SFDE) with memory driven by a fractional Brownian motion (fBm) with Hurst parameter H > 1/2. An Euler-type numerical scheme is proposed and analyzed under suitable regularity conditions on the drift and diffusion coefficients using tools from fractional calculus. We prove the convergence of the scheme and derive the corresponding rate in terms of the discretization step. Numerical simulations illustrate the theoretical results and confirm the accuracy of the proposed method.
Keywords Euler-Maruyama method, Fractional Brownian motion, Stochastic functional differential equations, Generalized Riemann–Stieltjes integral
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