Stationary and Integrated Autoregressive Neural Network Processes


We consider autoregressive neural network (ARNN) processes driven by additive noise. Suffcient conditions on the network weights (parameters) are derived for the ergodicity and stationarity of the process. It is shown that essentially the linear part of the ARNN process determines whether the overall process is stationary. A generalization to the case of integrated ARNN processes is given. Least squares training (estimation) of the stationary models and testing for non-stationarity are discussed. The estimators are shown to be consistent and expressions on the limiting distributions are given.

In Adaptive Information Systems and Modelling in Economics and Management Science working paper series
Adrian Trapletti
Adrian Trapletti

Quant, software engineer, and consultant mostly investment industry. Long-term contributor and package author R Project for Statistical Computing.