Hi Jean,
I understand that you are working on simulating a Moving Average (MA) process and need to verify its invertibility.
To assess this, you should examine the roots of the characteristic equation derived from the MA parameters, “theta_true”. The process is deemed invertible if all the roots of this equation lie outside the unit circle in the complex plane, meaning their absolute values exceed 1.
The “roots()” command should be applied to the characteristic equation based on the model parameters, “theta_true”, rather than to “y”. By focusing on the roots of this characteristic equation, you can effectively ensure that the invertibility condition is met.
You can also refer to the following MATLAB answer, which includes a relevant example: