How to estimate time series models with ARMA components by GMM

[Oliver Euvino]

I am trying to estimate a time series model by GMM. I had read everything about it and I understand how to use it, at least at a very basic level. I estimated some simple models without any problems, but I don´t know how to add a Moving Average (MA) component to my estimation. Adding lagged variables (as autoregresive components) is pretty simple, however I searched everywhere and I couldn´t find anything related to estimation of ARIMA models with GMM.

Somebody could help me how to add moving average components to a GMM estimation?

Thank you a lot.