Stationarity and Stability of Autoregressive Neural Network Processes

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

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Friedrich Leisch, Adrian Trapletti, Kurt Hornik


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.