Local Global Neural Networks
提出局部全局神经网络模型，涵盖现有非线性模型和混合专家方法，重点讨论线性专家情形下的平稳性、参数估计一致性和渐近正态性等理论性质，能描述间歇性动态，适用于生态、流行病和流体动力学等系统。
We propose the local-global neural networks model within the context of time series models. This formulation encompasses some already existing nonlinear models and also admits the mixture of experts approach. We emphasize the linear expert case and extensively discuss the theoretical aspects of the model: stationarity conditions, existence, consistency and asymptotic normality of the parameter estimates, and model identifiability. The proposed model consists of a mixture of stationary and nonstationary linear models and is able to describe “intermittent” dynamics; the system spends a large fraction of time in a bounded region, but sporadically develops an instability that grows exponentially for some time and then suddenly collapses. Intermittency is a commonly observed behavior in ecology and epidemiology, fluid dynamics, and other natural systems. A model-building strategy is also considered, and the parameters are estimated by concentrated maximum likelihood. The procedure is illustrated with two real time series.