LPC experiment

I created a MATLAB script which runs through 10000 tests. In each test
a random signal is created and IIR filtered. The IIR numerator is 1
and the IIR denominator is:

                         1
         -1.99240148160141
          3.01948286335539
         -2.81852242649452
          2.03872063706253
         -1.05454462109568
         0.414446268750399
        -0.115718625236828
        0.0224985092722183
       -0.0026689123535761
      0.000148764452177762

I analyze the output of the IIR filter using LPC analysis of some
order P which for each 10000 tests increments by 1 (from 1 to 30). For
each test I sum the variance of the error signal and once the 10000
tests have completed I calculate the mean error. I had expected to see
the mean error be at its minimum when the estimated model order
matched the true model order, but for some reason it bottoms at model
order = 7.

How come?



Here is the full matlab script:


clc
close all
clear all

% Unknown Linear Transfer Function
[b,a] = butter(10,0.4);
b = 1;

eVec = [];
for modelOrder = 1:30
    sumVarE = 0;
    for n = 1:10000
        filterInput = -0.05 + (0.05-(-0.05)).*rand(1,1000);
        filterOutput = filter(1,a,filterInput);
        % Estimate filter coefficients
        [est_a,est_e] = lpc(filterOutput,modelOrder);
        est_filterOutput = filter(1,est_a,filterInput);
        e = est_filterOutput - filterOutput;
        sumVarE = sumVarE + var(e);
    end
    sumVarE = sumVarE / 10000;
    eVec = [eVec sumVarE];

end
plot(1:30,eVec,'kx--')
drawnow