Time Series Approach to the Evolution of Networks: Prediction and Estimation

The article analyzes nonnegative multivariate time series which we interpret as weighted networks. We introduce a model where each coordinate of the time series represents a given edge across time. The number of time periods is treated as large compared to the size of the network. The model specifies the temporal evolution of a weighted network that combines classical autoregression with nonnegativity, a positive probability of vanishing, and peer effect interactions between weights assigned to edges in the process. The main results provide criteria for stationarity versus explosiveness of the network evolution process and techniques for estimation of the parameters of the model and for prediction of its future values. Natural applications arise in networks of fixed number of agents, such as countries, large corporations, or small social communities. The article provides an empirical implementation of the approach to monthly trade data in European Union. Overall, the results confirm that incorporating nonnegativity of dependent variables into the model matters and incorporating peer effects leads to the improved prediction power.