Stationarity and Stability of Autoregressive Neural Network Processes

Part of Advances in Neural Information Processing Systems 11 (NIPS 1998)

Authors

Friedrich Leisch, Adrian Trapletti, Kurt Hornik

Abstract

We analyze the asymptotic behavior of autoregressive neural net(cid:173) work (AR-NN) processes using techniques from Markov chains and non-linear time series analysis. It is shown that standard AR-NNs without shortcut connections are asymptotically stationary. If lin(cid:173) ear shortcut connections are allowed, only the shortcut weights determine whether the overall system is stationary, hence standard conditions for linear AR processes can be used.