This is a basic question on Box-Jenkins MA models. As I understand, an MA model is basically a linear regression of time-series values Y against previous error terms et,...,et−n. That is, the observation Y is first regressed against its previous values Yt−1,...,Yt−n and then one or more Y−Y^ values are used as the error terms for the MA model.

But how are the error terms calculated in an ARIMA(0, 0, 2) model? If the MA model is used without an autoregressive part and thus no estimated value, how can I possibly have an error term?

  • $\begingroup$ This questions has been asked several times before; see these questions. $\endgroup$ Sep 29, 2020 at 16:09
  • $\begingroup$ Another relevant thread is this. I was not able to find an excellent answer to your question, but with some effort this should be possible; the question is too common to not have an answer here. Indeed, there are several threads with relevant answers, you just have to find the best one for you. Otherwise, consult a time series textbook such as Hamilton "Time Series Analysis"; you will definitely find a detailed description of estimation of MA & ARMA models there. $\endgroup$ Sep 29, 2020 at 16:16


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