Dynamic modeling for multivariate functional and longitudinal data

Dynamic interactions among several stochastic processes are common in many scientific fields. It is crucial to model these interactions to understand the dynamic relationship of the corresponding multivariate processes with their derivatives and to improve predictions. In reality, full observations of the multivariate processes are not feasible as measurements can only be taken at discrete locations or time points, and often only sparingly and intermittently in longitudinal studies. This results in multivariate longitudinal data that are measured at different times for different subjects. We propose a time-dynamic model to handle multivariate longitudinal data by modeling the derivatives of multivariate processes using the values of these processes. Starting with a linear concurrent model, we develop methods to estimate the regression coefficient functions, which can accommodate irregularly measured longitudinal data that are possibly contaminated with noise. Our approach can also be applied to settings when the observational times are the same for all subjects. We establish the convergence rates of our estimators with phase transitions and further illustrate our model through a simulation study and a real data application.