Analysis of nonlinear dependences using artificial neural networks

In this paper, we develop a new technique for detecting nonlinear dependences in time series, based on the use of an autoregressive neural network and the concept of coefficient of correlation. Taking into account that the employed neural network model is able to approximate any function in a compact domain, the proposed measures are able to detect nonlinearities in the data. Our technique is tested for various simulated and real datasets, and compared with classical functions of simple and partial autocorrelations; the results show that the in the linear cases the proposed measures have a similar behaviour to the simple and partial autocorrelations, but in the nonlinear cases they are able to detect other nonlinear relationships.