NARX time delay estimation
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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!
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Accepted Answer
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
Greg
8 Comments
Greg Heath
on 13 Oct 2013
Several thoughts (but no conclusions):
1. Is this RW or a made up example?
2. It is not stationary. From the plot:
a. It looks like a running windowed mean would be quadratic or,at least, a low order polynomial.
b. A nth order polynomial is uniquely characterized by n+1 points and can be predicted by a linear, uniformly spaced,difference equation.
c. If the residual of a polynomial fit is Fourier analyzed, at least three points per period is needed to characterize each frequency component.
d. A sinusoid can be predicted by a linear, uniformly spaced difference equation.
e. Not sure about the corresponding running windowed variance.
3. If you have nothing to do some evening (e.g.,when your date doesn't show up) you might want to Fourier analyze a polynomial + sum of sinusoids model to try to understand how many feedback delays are sufficient.
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