Time series modeling on dynamic networks

Abstract

We consider multivariate time series on dynamic networks with a fixed number of vertices. Each component of the time series is assigned to a vertex of the underlying network. The dependency of the various components of the time series is modeled dynamically by means of the edges. We make use of 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, including of course an i.i.d. structure as is typically assumed in random coefficients models. Autoregressive moving average models are defined in this framework and stationarity conditions are discussed for network autoregressive models. Estimators of the parameters are discussed for various parameterizations of such network autoregressive models and how this can be used to forecast such a process. The finite sample behavior of the forecast approach is investigated and a real data example is presented.

Some recent trends in embeddings of time series and dynamic networks

“…The hope is that it will be amenable to statistical inference. Krampe (2019) treats dynamic networks with a fixed number of nodes, but where the dynamic structure is modeled by a doubly stochastic matrix.…”