Time series modeling on dynamic networks

Abstract

This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled by a multivariate doubly stochastic time series framework, that is we assume linear processes for which the coefficient matrices are stochastic processes themselves. We explicitly allow for dependence in the dynamics of the coefficient matrices as well as between the two stochastic processes driving the time series. This framework allows for a separate modeling of the attributes and the underlying network. In this setting, we define network autoregressive models and discuss their stationarity conditions. Furthermore, an estimation approach is discussed in a low- and high-dimensional setting and how this can be applied to forecasting. The finite sample behavior of the forecast approach is investigated. This approach is applied to real data whereby the goal is to forecast the GDP of $33$ economies.