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.

近年来，随着社交网络平台的增长，大量生成了诸如Facebook或Twitter之类的在线社交网络数据。网络时间序列模型的开发及其统计推断与社交网络技术及其演进的迅速发展一样重要。在这项工作中，我们考虑了Zhu等人提出的针对大型社交网络的网络矢量自回归。（Ann Stat 45（3）：1096-1123，2017），并研究其引导估计和引导预测。为了在基础模型中建议参数估计的引导程序版本，将两种引导程序方法组合在一起：固定引导程序和经典残差引导程序。建立自举估计器的一致性，并构造自举置信区间。而且，我们获得了多步未来值的自举预测间隔。蒙特卡洛（Monte-Carlo）研究表明，我们的自举技术比标准方法具有更好的有限样本性能。