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Predictions using NARX Network

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Pedro
Pedro on 22 May 2013
Answered: Dan on 1 Oct 2016
I am trying to build a network to do some long term predictions. My data is comprised of an INPUT and TARGET that spawns over 50 years (about 3500 points of data). At first I used the GUI to quickly get a network using default values. The network response seemed good but the ERROR Correlation and INPUT-ERROR cross correlation seem off( from what I understood from reading around here and the documentation, the peak should be at 0 lag). I tried adjusting the delays according to what I read in other question using the correlations but I don't understand how this works exactly. Where do I look to find the correct number of delays?
Another question I have is for long term predictions.Using the GUI I trained the network using around half of the data available, the network returned a very good approximation (with very little error between output and targets). Then in the next tab I used the TEST NETWORK and used the remaining points to see if it could predict the rest of the data. I would expect that at some point the error between output and target would grow but what I generally get is an excelent result where the output seems to be just a bit shifted under the target. (looks like the network learned everything when it is tested)
How can I correctly form predictions outside of the data I have?
I hope I was clear in my query.

Accepted Answer

Greg Heath
Greg Heath on 24 May 2013
You do not explain how you obtained your correlation functions.
Before you design a NARX, obtain the target-target autocorrelation function and the target-input cross-correlation function. Find the significant delays corresponding to peaks above the 95% confidence level of the cross-correlation of the target with random Gaussian noise
If you use nncorr, search my posts to avoid bugs in the code (e.g., the correct cross correlation function is not symmetric about zero lag).
greg nncorr
greg narxnet
Otherwise use ifft(conj(fft(x)).*fft(t)),or xcorr or crosscorr functions in other toolboxes .
The only thing that should have a peak at zero lag is the target autocorrelation function.
In order to predict future data, you need the preceding values of input and target to fill the delay buffers.
Hope this helps.
Thank you for formally accepting my answer
Greg
  3 Comments
Pedro
Pedro on 31 May 2013
"If the closed-loop doesn't work well on design data, it can be trained on the design data starting from the design that had been converted from open-loop."
Can you please clarify this for me?
For instance, I have data from 1 - 30. I train my open network until 20 and want to see if it predicts the remaining 10. Lets call it net1.
I close net1 and becomes net2 and simulate this new net with the new input. If the output is not good enough, I train net2 with the same data used with net1? Effectivly training the network again but now in close mode?
Thank you in advance.

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More Answers (2)

Greg Heath
Greg Heath on 31 May 2013
1. Design multiple open-loop (OL) nets in a double loop over the number of hidden nodes (outer loop) and random weight initializations(inner loop). For examples, search NEWSGROUP and ANSWERS with
greg Hub Ntrials
2. Use divideblock instead of dividerand to preserve correlations
3. Use the validation MSE tr.best_vperf to choose the best design and test MSE tr.best_tperf to estimate performance on unseen data.
4. To use the net on unseen data with only known inputs, convert the OL design to closed-loop (CL).
5. Evaluate the CL net on the design data.
6. If performance is significantly worse than the OL performance, use train to improve the CL performance.
7. Use the CL design with future inputs to predict future outputs.
8. If you know the corresponding future targets, you can evaluate the result.
Hope this helps.
Greg
  6 Comments
Dan
Dan on 1 Oct 2016
Xcsf, Acsf = Xcf, Acf ?
what do s and f stand for ( start, finish?)?

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