Functional Network Autoregressive Models for Panel Data

Abstract: This study proposes a novel functional vector autoregressive framework for analyzing network interactions of functional outcomes in panel data settings. In this framework, an individual's outcome function is influenced by the outcomes of others through a simultaneous equation system. To estimate the functional parameters of interest, we need to address the endogeneity issue arising from these simultaneous interactions among outcome functions. This issue is carefully handled by developing a novel functional moment-based estimator. We establish the consistency, convergence rate, and pointwise asymptotic normality of the proposed estimator. Additionally, we discuss the estimation of marginal effects and impulse response analysis. As an empirical illustration, we analyze the demand for a bike-sharing service in the U.S. The results reveal statistically significant spatial interactions in bike availability across stations, with interaction patterns varying over the time of day.