Problem with simulating an AR(2) process

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

rng(1);

% 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);
end    

The plot for the simulated resut shows an explosve pattern, being contradictary to the expection of a stationary process

% plot
plot(y, "-r")
yline(100) 

By using the econometric toolbox, this simulated results is stationary. So what is problem with my simulation program?

rng(1)
model2 = arima("constant", 30, "AR", [1.2, -0.5], "Variance", 1);

Y2 = simulate(model2, 200);

plot(Y2, "-r")
yline(100)

Answer 1

[Ferry]

It's true! Thanks a lot!

Answer 2

[Pavan Guntha]

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!

[Ferry]

It's true! Thanks a lot!