Time series: theory and methods
Time series: theory and methods
Multilayer feedforward networks are universal approximators
Neural Networks
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Stationarity and stability of autoregressive neural network processes
Proceedings of the 1998 conference on Advances in neural information processing systems II
Long-range out-of-sample properties of autoregressive neural networks
Neural Computation
Anomaly detection in streaming environmental sensor data: A data-driven modeling approach
Environmental Modelling & Software
Boosting GARCH and neural networks for the prediction of heteroskedastic time series
Mathematical and Computer Modelling: An International Journal
Nonlinearity in Forecasting of High-Frequency Stock Returns
Computational Economics
Hi-index | 0.00 |
We consider autoregressive neural network (AR-NN) processes driven by additive noise and demonstrate that the characteristic roots of the shortcuts-the standard conditions from linear time-series analysis-determine the stochastic behavior of the overall AR-NN process. If all the characteristic roots are outside the unit circle, then the process is ergodic and stationary. If at least one characteristic root lies inside the unit circle, then the process is transient. AR-NN processes with characteristic roots lying on the unit circle exhibit either ergodic, random walk, or transient behavior. We also analyze the class of integrated AR-NN (ARI-NN) processes and show that a standardized ARI-NN process "converges" to a Wiener process. Finally, least-squares estimation (training) of the stationary models and testing for nonstationarity is discussed. The estimators are shown to be consistent, and expressions on the limiting distributions are given.