Issues in generating AR model with a constraint

Question

I am new to the topic of system identification and looking for a large Autoregressive (AR) model. Can anybody point out a large stable AR model which has more than 2 coefficients AND there should be a large number of zero coefficients?

This link presents an example of how to have nonzero coefficients in lag 1,4 for order, $p=4$ AR(4) model. But, the values are NaN !! So, how do I apply this technique so as to generate a large AR model with more number of zero coefficients and lesser number of non-zero coefficients ?

EDIT:

Looking for any stable AR($p$) model (preferably popular cited ones, if available) of higher order $p \ge 20$ where the number of non-zero coefficients are few (constraint) . If I generate a noisy sinusoidal wave given below, then

%Generate sine wave = A*sin(2*pi*f*t + phi)
t = linspace(0,1,1000);
A = 5;
f = 2;
phi = pi/8;
sinewave = A*sin(2*pi*f*t + phi);
noisy_sine=sinewave+0.5*randn(size(t));
subplot(1,2,1);
plot(t, sinewave)
hold on;
subplot(1,2,2);
plot(t,noisy_sine);

%Generate AR model
order =20;
ARCoeff = aryule(noisy_sine,order);

It returns AR model of 20 lags. But, all the coefficients are non-zero. How do I generate AR model of any order higher than 2 where the number of non-zero coefficients are lesser than the number of zero coefficients ?

Answer 1

I was able to produce the AR(p) model with much of zero-coefficients. I use Scilab rather than Matlab, therefore I'll just describe the technique:

• Generate some appropriate data with the desired spectral properties - the AR model will mimic these spectral properties.
• Fit the AR model of the desired order to your data.
• Find the desired number of the coefficients with the lowest values and reset them to zero
  (something like a(find(abs(a) < stdev(a) / 2)) = 0 - valid in Scilab).

The resulting model should (may?) still has a similar spectral properties & satisfy your requirements considering zero-coefficients.