We study general nonlinear models for time series networks of integer and continuous valued data. The vector of high dimensional responses, measured on the nodes of a known network, is regressed non-linearly on its lagged value and on lagged values of the neighboring nodes by employing a smooth link function. We study stability conditions for such multivariate process and develop quasi maximum likelihood inference when the network dimension is increasing. In addition, we study linearity score tests by treating separately the cases of identifiable and non-identifiable parameters. In the case of identifiability, the test statistic converges to a chi-square distribution. When the parameters are not-identifiable, we develop a supremum-type test whose p-values are approximated adequately by employing a feasible bound and bootstrap methodology. Simulations and data examples support further our findings.

翻译：我们研究了整数值和连续值时间序列网络数据的一般非线性模型。在已知网络的节点上测量的高维响应向量，通过使用平滑链接函数，对其滞后值及相邻节点的滞后值进行非线性回归。我们研究了此类多元过程的稳定性条件，并在网络维度递增时发展了拟极大似然推断方法。此外，我们分别处理了参数可识别与不可识别的情形，研究了线性得分检验。在可识别情形下，检验统计量收敛于卡方分布。当参数不可识别时，我们发展了一种上确界型检验，其p值可通过可行的界及自举方法得到充分近似。模拟实验与数据实例进一步支持了我们的发现。