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NARX (Nonlinear AutoRegressive with eXogenous inputs) with neural networks

NARX (Nonlinear AutoRegressive with eXogenous inputs) is a model for time series forecasting. It can be modeled with Neural Networks.

The main idea it uses is the following: create an architecture that feeds three types of inputs to the learning algorithm: the past input values of the time series, the past predicted values by the model itself, and exogenous variables - a different time series that indirectly affects the time series we want to predict ( there can be more ).

All the inputs are being fed to a simple neural network architecture that is based on BPTT ( back propagation through time ) and TDNN (time delay neural networks ).

I started working on this subject on my master thesis at Universitat Polytecnica de Catalunya, Barcelona, Spain.

You can visit my project on Sourceforge.

Most important articles about NARX:

T. Lin, B. G. Horne, P. Tino, and C. L. Giles, “Learning long-term dependencies in NARX
recurrent neural networks.,” IEEE transactions on neural networks / a publication of the
IEEE Neural Networks Council, vol. 7, no. 6, pp. 1329-38, Jan. 1996.

H. T. Siegelmann, B. G. Horne, and C. L. Giles, “Computational capabilities of recurrent NARX
neural networks.,” IEEE transactions on systems, man, and cybernetics. Part B,
Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society, vol. 27, no.
2, pp. 208-15, Jan. 1997.

J. Menezesjr and G. Barreto, “Long-term time series prediction with the NARX network: An
empirical evaluation,” Neurocomputing, vol. 71, no. 16-18, pp. 3335-3343, Oct. 2008.

E. Diaconescu, “The use of NARX neural networks to predict chaotic time series,” WSEAS
Transactions on Computer Research, vol. 3, no. 3, pp. 182–191, 2008.