Long Memory via Networking

Abstract

Many time-series data are known to exhibit "long memory", that is, they have an autocorrelation function that decays very slowly with lag. This behavior has traditionally been attributed to either aggregation of heterogenous processes, nonlinearity, learning dynamics, regime switching, structural breaks, unit roots or fractional Brow-nian motion. This paper identifies an entirely different mechanism for long memory generation by showing that it can naturally arise when a large number of simple linear homogenous economic subsystems with a short memory are interconnected to form a network such that the outputs of each of the subsystem are fed into the inputs of others. This networking picture yields a type of aggregation that is not merely additive , resulting in a collective behavior that is richer than that of individual subsystems. Interestingly, the long memory behavior is found to be almost entirely determined by the geometry of the network while being relatively insensitive to the specific behavior of individual agents.