Time series, wavelets, high dimensional data and applications

Abstract

This project is a natural follow-up to an ongoing project 18/04654-9, which is the most recent of a series of thematic projects from this research group endowed by FAPESP in the last twenty years. The proposed statistical methodologies will have application in Medicine, Finance, Biology, Physics, Neurosciences, Engineering, among others areas. They solve theoretical and empirical questions, in the following topics, in a mostly interwoven manner: (1) Generalizations of ARMA, processes, (2) Wavelet methods, (3) Quasi U-statistics, (4) Extreme values in time series, (5) Volatility modeling in financial data, including high-frequency data, (6) Functional data analysis, (7) high dimensional data, with focus on time series, spacial-temporal data, financial series, satellite image analysis, genetics, MRI and fNRIS. Besides the scientific output on the form of published papers in highly selective international journals and presentation in international meetings, the project should result in highly skilled young researchers, through post-doctoral, doctoral, masters, and undergraduate work supervisions. In order to ascertain the state-of-the-art status of the aforementioned research, periodical seminars and annual internationals workshops will be held, as well as visits from the Brazilian team members to world centers, and to the Brazilian institutions by international research leaders. (AU)