Estimation of a Measure of Local Correlation for Independent Samples and Time Series Data

Different from measures of global dependence, measures of local dependence evaluate the dependence along the support of the variables. The aim of this paper is to study a measure of local dependence proposed by Bairamov et al. (2003) in the context of variables not indexed by time and also for stationary time series. We propose similar estimators for both cases. The consistency of the estimators are obtained, and their behaviour are studied through simulations. Some empirical illustrations are provided.