- 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
Presample states for ARMA model, Question for function arima and simulate
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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.
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Answers (1)
Shashank Prasanna
on 11 Nov 2013
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).
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