Generalized Linear Models Network Autoregression

We discuss a unified framework for the statistical analysis of streaming data obtained by networks with a known neighborhood structure. In particular, we deal with autoregressive models that make explicit the dependence of current observations to their past values and the values of their respective neighborhoods. We consider the case of both continuous and count responses measured over time for each node of a known network. We discuss least squares and quasi maximum likelihood inference. Both methods provide estimators with good properties. In particular, we show that consistent and asymptotically normal estimators of the model parameters, under this high-dimensional data generating process, are obtained after optimizing a criterion function. The methodology is illustrated by applying it to wind speed observed over different weather stations of England and Wales.