NARX time delay estimation

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Rad on 7 Aug 2013
Commented: Rad on 24 Oct 2013
Hello, I’m trying to determine the feedback and input delays for a 3-input 1-output NARX network using target-target auto-correlation and input/target cross-correlation, respectively. For each input/target pair, the max. cross-correlation (peak) value occurs at a different lag. Given that all input delays must be the same for a NARX network, which value out of the 3 different lags should I select? The smallest one?
For the target-target auto-correlation, the max. lag is at 0, and the value of the auto-correlation coefficients decreases as the number of lags increase. How is the proper feedback delay selected in this case?
Sorry if these questions seem trivial; any help would greatly be appreciated. Thank you!

Accepted Answer

Greg Heath
Greg Heath on 10 Aug 2013
Consider all lags that are significant.
If your cross-correlation function does not output significance levels, consider my approach for the 95% confidence level:
1. Order the absolute values of the cross-correlation between zscore(t,1) and zscore(randn(1,N),1).
2. Choose the value at floor(0.95*(2*N-1)).
3. Repeat 100 or more times and average the result.
4. Design a timedelaynet and only keep as many significant input delays as you need.
5. Design a narnet and only keep as many significant feedback delays as you need.
6. Design a narxnet using the delays obtained in 4 and 5.
If you search using the word NNCORR you will find many of my examples
Thank you for formally accepting my answer
Rad on 24 Oct 2013
Thank you so much for all your help, it is greatly appreciate it. I'll look into your recommendations and I'll post my results when I'm done. Once again, thank you!

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