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On the Consistency of the Blocked Neural Network Estimator in Time Series Analysis

alex.sarishvili{at}itwm.fraunhofer.de Institute of Industrial Mathematics, Kaiserslautern, Germany

Ch. Andersson

christina.andersson{at}esi.oru.se Department of Economy, Statistics, and Computer Science, University of Örebro, Sweden

J. Franke

franke{at}mathematik.uni-kl.de Department of Mathematics, University of Kaiserslautern, Germany

G. Kroisandt

gerald.kroisandt{at}itwm.fraunhofer.de Institute of Industrial Mathematics, Kaiserslautern, Germany

We describe a nonlinear regression problem, where the regression functions have an additive structure and the dependent variable is a one-dimensional time series. Multivariate time series with unknown time delay operators are used as independent variables. By fitting a feedforward neural network with block structure to the data, we estimated the additive regression function and, parallel to this, the time lags. We present the consistency proof of neural network weights estimator and the time lag estimator independently from each other. In the practical part of the article, we present the useful feature of blocked neural networks to estimate the relevance measures of each input variable in a simple way. Furthermore, we propose an approach to solve the well-known variable selection problem for the class of nonlinear multivariate beta-mixing time series models considered here. Finally, we apply the methodology to an artificial example.