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.
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1See this question ARIMA Estimation by Hand answers your question on MA component using MLE. – forecaster Jul 05 '20 at 15:56
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Did my comment help? – forecaster Jul 06 '20 at 15:23
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1This 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