Issues in generating AR model with a constraint
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) &lt; stdev(a) / 2)) = 0 - valid in Scilab).


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