How the error is generated in MA process?

Question

If a time series process depends on its own past values then it's a AR process. These is what i understood but if it depends on it's own error then it's a MA process. Here is where i get confused.
Today = mean + Noise + slope(yesterday's error)

How these error got generated beforehand? Error is when a time series is forecasted using any forecasting model and then Actual - forecasted gives error.MA model regressed on these error.Is these the same error we consider in MA. If yes then how these error are generated first in MA?
I got stuck here.

Although got some nice references below one to be specific but not able to understand intuitively. Moving Average (MA) process: numerical intuition

Thanks

Answer 1

In theory, a stationary process has an MA representation and an AR representation. For example, an MA(1) process can be represented as AR($\infty$) and AR(1) can be written as an MA($\infty$) process.

In practice, given an MA(1), there is an AR(n) with a high order that works similarly. However, when we fit AR(n), we may have may too many parameters to estimate from the sample and MA(1) gives us the best parameter estimation. It is usually AR and MA combined (ARMA process) that give us the most parsimonious model.