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

Adrian Trapletti, Friedrich Leisch, Kurt Hornik

Publikation: 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.
OriginalspracheEnglisch
ErscheinungsortVienna
HerausgeberSFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business
PublikationsstatusVeröffentlicht - 1999

Publikationsreihe

NameWorking Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
Nr.37

WU Working Paper Reihe

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

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