How can I calculate the parameters of a MA time series model? I am new to Time Series Analysis and I have problems understanding the MA-model (opposed to the AR model). I read many webpages about it and it is either said that MA is a linear regression with past forecast errors or with white noises. So some label the Epsilons as past forecast errors and others as white noise.
My question is whether there is a difference between those two 'approaches'? Further, I do not understand how we can calculate the forecast errors. As far as I understood MA is used for forecasting itself. So how can I fit a forecasting model that itself relies on an forecast (of past error terms)? So my basic question is how can I calculate the Epsilon-parameters of the MA model?
I'd appreciate every comment.
EDIT: Do you know a website where the MA model is explained in an understandable ways also for people who have just started to learn and use time series? I still do not know  how I can calculate the parameters.
 A: 
My question is whether there is a difference between those two [AR and MA]
'approaches'?

Any stationary $AR(p)$ process have an $MA(\infty)$ representation, and any invertible $MA(q)$ process have an $AR(\infty)$ representation.

Further, I do not understand how we can calculate the forecast errors

I give here (Is the MA($\infty$) process with i.i.d. noise strictly stationary?) a formula for the variance of an $MA(q)$ process. In is estimated version, if there aren't bias problems, it represent an estimate of mean square forecast error also (MSFE).

So how can I fit a forecasting model that itself relies on an forecast
(of past error terms)? So my basic question is how can I calculate the
Epsilon-parameters of the MA model?

Actually an $AR(p)$ model can be estimated consistently in standard OLS fashion also, while $MA(q)$ are not. This happen because the "error series" is not observable. In most software some ML algorithm are implemented; some theoretical points are addressed here:  https://www.it.uu.se/research/publications/reports/2006-022/2006-022-nc.pdf
