Nonlinear network autoregression
研究了整数和连续值时间序列网络的非线性模型，提出了稳定性条件和拟极大似然推断方法，并针对可识别和不可识别参数分别开发了线性检验统计量。
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 nonlinearly 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 nonidentifiable 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.