Georgia Institute of Technology College of Sciences

Applicability of Pearson's correlation as a measure of explained variance is by now well understood. One of its limitations is that it does not account for asymmetry in explained variance. Aiming to obtain broad applicable correlation measures, we use a pair of r-squares of generalized regression to deal with asymmetries in explained variances, and linear or nonlinear relations between random variables. We call the pair of r-squares of generalized regression generalized measures of correlation (GMC). We present examples under which the paired measures are identical, and they become a symmetric correlation measure which is the same as the squared Pearson's correlation coefficient. As a result, Pearson's correlation is a special case of GMC. Theoretical properties of GMC show that GMC can be applicable in numerous applications and can lead to more meaningful conclusions and decision making. In statistical inferences, the joint asymptotics of the kernel based estimators for GMC are derived and are used to test whether or not two random variables are symmetric in explaining variances. The testing results give important guidance in practical model selection problems. In real data analysis, this talk presents ideas of using GMCs as an indicator of suitability of asset pricing models, and hence new pricing models may be motivated from this indicator.