Asymptotic Theory Under Network Stationarity

This paper develops an asymptotic theory for network data based on the concept of network stationarity, explicitly linking network topology with the dependence be-tween network entities. Each pair of entities is assigned a class based on a bivariate graph statistic. Network stationarity assumes that conditional covariances depend only on the assigned class. The asymptotic theory, developed for a growing network, includes laws of large numbers, consistent autocovariance function estimation, and a central limit theorem. A significant portion of the assumptions concerns random graph regularity conditions, particularly those related to class sizes. Weak dependence assumptions use conditional –-mixing adapted to networks and based on the assigned classes instead of Euclidean space distances. A network-robust standard errors estimator is proposed. The framework is illustrated through an application to microfinance data from Indian villages.