Patrick is graduated in accounting from the University Center of Espirito Santo (Brazil) and mathematics from the Federal University of Espírito Santo - UFES (Brazil), and a Master's degree in Economics from the UFES (Brazil). Currently, Patrick is a PhD student at Universite Paris-Saclay - CentraleSupelec (France) and at the Department of Environmental Engineering of UFES. His research fields of interest are: time series analysis (in the time and frequency domains), forecasting, econometric modelling, robustness in time series, multivariate time series, environmental and econometrics data analysis, linear and non-linear regression with time series covariates, quantile regression and differential equations.

L2S, CentraleSupélec
3 rue Joliot Curie
91190 Gif-sur-Yvette, France

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Thesis title: M-quantile approach for heteroscedastic processes.

Short description: this PhD thesis aims to extend the applicability of quantile and M-estimation methods to parameter estimation in conditional heteroscedastic processes. While quantile and M-estimators are renowned for their robustness to outliers and their wide use in estimating various time series models with diverse correlation structures, this research aims to generalize these techniques into the domain of M-quantile estimation for both univariate and multivariate heteroscedastic parametric models. This thesis focuses on time series data characterized by time-dependent variance (volatility), a well-studied area within econometrics and finance. Our practical motivation is to develop models and forecasting methods for real-world problems in econometrics and air quality. Specifically, we aim to address challenges related to variables such as log returns and air pollution data, exhibiting time-dependent mean and variance in the context of econometrics and air quality, respectively. This research seeks to contribute valuable insights and methodologies to enhance the modelling and prediction of these critical variables.

Keywords: M-regression, quantile, outliers, heteroscedasticity, pollution and finance.

Start date: 01/12/2021.

Name and affiliation of supervisors: Pascal Bondon (Paris-Saclay) and Valderio Reisen (Federal University of Espirito Santo).