# Different results for different orders of estimating AR model using Yule-Walker equations

I'm trying to use MATLAB to estimate the AR parameters to the following filter:

$$H(z) = \frac{1}{1-0.5z^{-1}+0.25z^{-2} -0.25z^{-4}}$$ As I can see, the process at the output of this filter depends on the previous 4 samples. So, i figured that i would need 4th order model of Yule-Walker equations.

I run a MATLAB code solving Yule-Walker equations for 4,8,16,64 order and when I compared the 4 options, I got that the higher the order, the higher the MSE error. How can i explain this fact?

Here is a plot I got when compared $\lvert S(w)-S_{\rm estimated}(w)\rvert^{2}$.

• Did you expect the error to be lower for higher order? I'm not quite sure I see the point of the question. Assuming more parameters in your model (when the model matches the true system) generally results in higher errors. You might get lucky, but those higher order terms generally don't go to zero and so add to the difference from the true model. – Peter K. May 28 '16 at 21:00
• "Assuming more parameters in your model (when the model matches the true system) generally results in higher errors" Can you please explain why is this happening? – user3921 May 29 '16 at 16:02
• Your true AR model is order 4. If an AR(16) model did a good job, then 12 of its parameters should be zero. Because of noise effects / overfitting, those 12 parameters are NOT zero and, more than likely, the other matching parameters will be more inaccurate because of this. Hence the error in an AR(16) will be larger than that for an AR(4) fit. – Peter K. May 29 '16 at 16:07