On the ergodicity and stationarity of the ARMA (1,1) recurrent neural network process

Adrian Trapletti, Friedrich Leisch, Kurt Hornik

Publication: Working/Discussion PaperWU Working Paper

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Abstract

In this note we consider the autoregressive moving average recurrent neural network ARMA-NN(1, 1) process. We show that in contrast to the pure autoregressive process simple ARMA-NN processes exist which are not irreducible. We prove that the controllability of the linear part of the process is sufficient for irreducibility. For the irreducible process essentially the shortcut weight corresponding to the autoregressive part determines whether the overall process is ergodic and stationary.

Publication series

SeriesWorking Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
Number37

WU Working Paper Series

  • Working Papers SFB \Adaptive Information Systems and Modelling in Economics and Management Science\

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