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I understand that the AR models can be estimated with both OLS and MLE, since all the values of the time series are known. However, I don't understand how the parameters for the MA parts can be estimated with MLE, as I found in literature. The error terms are unknown, so there aren't any data to maximise to find the most likely parameter. Any help to explain this point will be appreciated.

Richard Hardy
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Anna
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    See this question [ARIMA Estimation by Hand](https://stats.stackexchange.com/questions/77663/arima-estimation-by-hand) answers your question on MA component using MLE. – forecaster Jul 05 '20 at 15:56
  • Did my comment help? – forecaster Jul 06 '20 at 15:23
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    This is standard time-series textbook material. Try Hamilton "Time Series Analysis" or almost any other time series textbook at a sufficiently high technical level. There are also plenty of lecture notes available online discussing the question. – Richard Hardy Jul 08 '20 at 18:52

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