Presample states for ARMA model, Question for function arima and simulate

I read the function "simulate" ( http://www.mathworks.com/help/econ/arima.simulate.html). This function says the following:

% % The user did not specify presample y(t) observations. %

   if isARstable && (sum(AR) ~= 1) && ~isRegressionIncluded
%
%     The model is AR-stable and without a regression component, so compute 
%     the unconditional (i.e., long-run) mean of the y(t) process directly 
%     from the parameters of the model and use it to initialize any required 
%     presample observations.
%
      average = constant / (1 - sum(AR));
      Y       = repmat([average(ones(1,maxPQ)) zeros(1,numObs)], numPaths, 1);

   else
%
%     The model is not AR-stable, and so a long-run mean of the y(t) process 
%     cannot be calculated from the model. The following simply assumes zeros 
%     for any required presample observations for y(t).
%
      Y  = zeros(numPaths,T);

   end

Could someone please help me to understand why this is true. I dont understand the idea.

Answer 1

[Shashank Prasanna]

Case 1: If the lag order polynomial has mag of all roots < 1, it is stable.

e.g: y(t) = 0.9*y(t-1) + e

The AR model won't blow up with time. Which means its assumed OK to take the series mean as presamples.

Case 2: The the lag order polynomial is unstable. the AR model will blow up with time.

e.g: y(t) = 1.1*y(t-1) + e

This means it may not be reasonable to use the sample mean as presamples for an unstable time series (which approaches infinity over time).

• If this automatic choice is of concern you may provide your own presamples
• I am not certain, but this information may be mentioned in the books specified in the references section of the documentation page scroll down