Bootstrap inference for network vector autoregression in large-scale social network

A large amount of online social network data such as Facebook or Twitter are extensively generated by the growth of social network platforms in recent years. Development of a network time series model and its statistical inference are as important as the rapid progress on the social network technology and evolution. In this work we consider a network vector autoregression for the large-scale social network, proposed by Zhu et al. (Ann Stat 45(3):1096–1123, 2017), and study its bootstrap estimation and bootstrap forecast. In order to suggest a bootstrap version of parameter estimates in the underlying model, two bootstrap methods are combined together: stationary bootstrap and classical residual bootstrap. Consistency of the bootstrap estimator is established and the bootstrap confidence intervals are constructed. Moreover, we obtain bootstrap prediction intervals for multi-step ahead future values. A Monte-Carlo study illustrates better finite-sample performances of our bootstrap technique than those by the standard method.