Wavelet Analysis of Functional Data - Applications in Econometrics
Time series, wavelets, high dimensional data and applications
Statistical analysis of temporal graph wavelets statistical analysis of temporal g...
Abstract
In this project we will investigate methodologies of time series, wavewlets and functional data analysis, with potential applications in several fields, as medicine, biology, physical sciences, chemistry, actuarial sciences, finance, etc. These methodologies aim to solve some important theoretical and applied problems related to the following strongly connected research topics: 1. Evaluation of risks associated with events as increase in temperature and sea level, melting of glaciers, deforestation, earthquakes and also with measures of risks in economics and finance. 2. Occurrences of extreme values in time series and characterization of extreme dependences. 3. Estimation of volatilities of financial assets, including high frequency data. 4. Extension of the concept of copula to the case of time series, dynamical copulas and application to the study of the dependence. 5. Study of processes with long dependence, with applications in physical sciences, economics and finance. 6. Functional data analysis, with emphasis in regression models, FANOVA models, spectral analysis, etc. 7. Applications to the study of sequences of DNA, microarrays, functional magnetic resonance imaging. (AU)
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