NONLINEAR NETWORK AUTOREGRESSION

• 成果类型: Article
• 署名作者: Armillotta, Mirko; Fokianos, Konstantinos
• 署名单位: Vrije Universiteit Amsterdam; University of Cyprus
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2345
• 发表日期: 2023
• 页码: 2526-2552
• 关键词: weak dependence conditions; time-series; nuisance parameter; models; tests; specification; Consistency; linearity; inference; LAW

摘要

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 sepa-rately 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.