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Local global neural networks: a new approach for nonlinear time series modeling. (English) Zbl 1055.62106
Summary: We propose a 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.

MSC:
62M45 Neural nets and related approaches to inference from stochastic processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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