【12月19日】【统计与数学学院学术论坛】Generalized Measures of Correlation and Their Implications in GARCH and Heston发布日期：2019-09-12 21:12:22
报告题目：Generalized Measures of Correlation and Their Implications in GARCH and Heston Models
威斯康星大学统计系副教授、副主任；北卡罗来纳大学教堂山分校统计学博士，北京航空航天大学管理工程博士。美国统计学会、数理统计学会等多个学会会员，曾获得University of North Carolina教学奖等多项奖励，2010年入选剑桥名人录。主持有10余项美国自然科学基金等科研课题；在JASA等顶级统计学期刊发表学术论文50余篇。同时担任Journal of Business and Economic Statistics等多个国际著名统计学期刊的副主编。
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.