Local and global temporal correlations for longitudinal data

Quantifying the association between a pair of random functions recorded over a time period is of general interest. Several methods have been proposed in the literature but they either suffer from an ill-posed problem intrinsic to functional data or are suitable only for intensely recorded longitudinal data. In this paper we provide new methods that overcome these challenges by investigating the temporal Pearson correlation between paired random functions. We investigate both a local temporal correlation measure and a global summary measure of the dynamic temporal correlations and propose a nonparametric estimation method that covers both intensely observed and sparsely observed longitudinal data. Asymptotic results of the estimators are derived under mild conditions and the method is illustrated via simulations and a benchmark data set.