Desenvolvimento de um método para a quanticação da associação instantânea multivariável

Abstract

This work presents a method for quantifying the instantaneous association between two groups of variables. This association can be assessed in different ways and it is usually dependent on each applications specic goals. In this work, three measures are dened. The rst one (v) captures the shared variance between the groups of variables by mapping the linear relationship between them. In order to establish each groups total variance, Principal Component Analysis (PCA) and Canonical Component Analysis (CCA) are used to remove redundant information by diagonalizing the covariance matrix. The use of CCA provides two additional denitions of association: one that estimates the probability of the two groups being independent (h) and another one where the association is dened as the maximum correlation found between the groups (c). Time-varying uctuations are captured by using an exponential moving average lter to estimate the covariance between variables. The proposed method was tested on three databases; two collected during speech production experiments and one consisting of time series of stock prices. The method was able to detect how the association changes over time, to establish the impact of each variable over the global association measure, and to detect delays between the domains.