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Problem with simulating an AR(2) process

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Ferry el 12 de Oct. de 2021
Respondida: Ferry el 21 de Oct. de 2021
I'm new in Matlab. I‘m trying to simulate a second-order autoregressive process which is stationary, but end up with an explosive pattern. I don't know why I cannot get it right. The process I simulate is
I made the following programm to simulate it for 200 periods, with initial values
% parameters
rhho2 = [30, 1.2, -0.5];
% preallocation
N = 200 ;
y = zeros(N, 1);
y(1:2, :) = [100; 100];
% innovation
innovation = randn(200, 1);
for t = 3 : N
y(t, :) = rhho2 * [1; y([t-2, t-1], :)]+ innovation(t, 1);
The plot for the simulated resut shows an explosve pattern, being contradictary to the expection of a stationary process
% plot
plot(y, "-r")
By using the econometric toolbox, this simulated results is stationary. So what is problem with my simulation program?
model2 = arima("constant", 30, "AR", [1.2, -0.5], "Variance", 1);
Y2 = simulate(model2, 200);
plot(Y2, "-r")

Respuesta aceptada

Ferry el 21 de Oct. de 2021
It's true! Thanks a lot!

Más respuestas (1)

Pavan Guntha
Pavan Guntha el 20 de Oct. de 2021
Hello Ferry,
The reason for mismatch in the outputs is due to the misordering in the following equation:
y(t, :) = rhho2 * [1; y([t-2, t-1], :)]+ innovation(t, 1);
This is supposed to be as follows as per the equation presented in the question:
y(t, :) = rhho2 * [1; y([t-1, t-2], :)]+ innovation(t, 1);
Hope this helps!


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