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 $\lvert S(w)-S_{\rm estimated}(w)\rvert^{2}$.