# How to determine the order of ARMA and AR coefficient ?

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Husni on 19 Nov 2012
Commented: Magdy Ismail on 14 Feb 2021
Perhaps this is very simple question. I have been trying to find it. How can we determine the order of ARMA and AR coefficient in Matlab? What I mean here is not merely trial and error.
Any suggestion is appreciated
Sincerely yours
Ali
Magdy Ismail on 14 Feb 2021
Did you find an answer for your problem because i am searching for the same thing how to determine the order of AR model?

Rajiv Singh on 20 Nov 2012
One way would be to state-space estimation which lets you inspect the Hankel singular values for model order:
% pick optimal order in the 1:10 range: model = n4sid(data, 1:10);
HF on 21 Oct 2020
Hello, I was trying to apply your code into my Matlab file. Unfortunately, it is not working. Any suggestions in how to fix. I would really appreciate that.
This is my code:
Fs = 1000;
max_freq = 20;
value = 500;
signal = e(1:value);
m = n4sid(signal, 1:10);
order = idpoly(m)
[X, Y] = pyulear(e_test,order,length(e_test),Fs);

Gurudatha Pai on 12 Dec 2012
Model order selection is often a tricky business. Inspecting the Hankel singular values is one many methods. There are many such methods, arguably one as good or worse as the other.
Specifically in the case AR/ARMA models, you may look into the model residues. Specifically, if you have used a "sufficient" model orders, the residuals should look white. Note that the residuals may look white for many model order selections. There are statistical hypothesis testing procedures (e.g. Chi-2 test, etc.) for both sample auto-correlation of residuals and cross-correlation of residuals and input; Ljung's book has a lot of details on all of this.
Hope that helps.