ρDCCA e DMC2 x : Implementação, Otimização e Aplicações

Abstract

This thesis presents an investigation into the analysis of time series through the functions DF A, DCCA and, mainly, the coefficients ρDCCA and DMC2 x. It presents a bibliographic research focused on methods based on DF A that treat multi-correlation and the applications of these functions and coefficients in Environmental Sciences. We also present articles produced in the process of this thesis, dealing with the application of the coefficients ρDCCA and DMC2x. The implementation of a computational tool (the Python Zebende library) for manipulating time series and calculating the functions and coefficients is presented, as well as the Detrended Saved algorithm, an innovative strategy in the general calculation of DCCA, but with advantages in performance when used for calculations of many series among themselves (such as in the case of matrix construction of ρDCCA to calculate DMC2x, when a large number of time series is used). The capacity of the Zebende library to enhance the use of these coefficients is also presented.