CHOLLETE, Loran; HEINEN, Andréas; VALDESOGO, Alfonso - Center for Operations Research and Econometrics (CORE), … - 2008
relations and will therefore miss non-linear relations between variables.
Consider, for example two variables X and Y, where X … » N(0;1) and Y = X2. In this
setup, Cov(X;Y) = Cov(X;X2) = Skewness(X). Therefore X and Y are uncorrelated,
since their … covariance is equal to the skewness of X, which is 0, by normality of X. Yet,
clearly these variables are perfectly dependent …