TY - JOUR
T1 - Local global neural networks
T2 - A new approach for nonlinear time series modeling
AU - Suárez-Fariñas, Mayte
AU - Pedreira, Carlos E.
AU - Medeiros, Marcelo C.
N1 - Funding Information:
Mayte Suárez-Fariñas is Postdoctoral Fellow, Center for Studies in Physics and Biology, The Rockefeller University, New York, NY (E-mail: [email protected]). Carlos E. Pedreira is Associate Professor, Department of Electrical Engineering (E-mail: [email protected]), and Marcelo C. Medeiros is Assistant Professor, Department of Economics (E-mail: [email protected]), Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil. This work is based on the first author’s doctoral thesis at the Department of Electrical Engineering, Pontifical Catholic University, Rio de Janeiro. Financial support from the CNPq is gratefully acknowledged. The authors thank Marcelo O. Magnasco, Maurício Romero Sicre, Juan Pablo Torres-Martínez, and Alvaro Veiga for valuable discussions and two anonymous referees, an associate editor, and the editor for helpful comments.
PY - 2004/12
Y1 - 2004/12
N2 - 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.
AB - 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.
KW - Model building
KW - Model identifiability
KW - Neural network
KW - Nonlinear model
KW - Parameter estimation
KW - Sunspot number
KW - Time series
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U2 - 10.1198/016214504000001691
DO - 10.1198/016214504000001691
M3 - Article
AN - SCOPUS:10844281822
SN - 0162-1459
VL - 99
SP - 1092
EP - 1107
JO - Journal of the American Statistical Association
JF - Journal of the American Statistical Association
IS - 468
ER -