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I have the following problem of detecting the MA order in usage of the ACF plot. enter image description here

Note: The process is stationary and the lags display monthly data.

I am not really able to say which order suits the data the best. In my opinion I could find argues for MA1 till MA12 and maybe even further.

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    $\begingroup$ Consider using an AR or ARMA model instead. You will end up with a much more parsimonious model than a pure MA. $\endgroup$ Jan 3 at 18:58

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With a stationary process, we can determine our $q$ parameter of the appropriate MA model by the number of significant lags in the ACF. The dotted-blue lines indicate the upper and lower limits for insignificant lags (based on the user-inputted confidence levels or default settings).

Some model comparison is ultimately necessary to figure out the best model due to differences in interpretation of the ACF lags. For instance, I would first compile an MA(14) model because I see the first 14 lags are each significant. Some discretion between using $q$ = 13 or 14 is necessary depending on how much you'd like to discriminate on significance. Many people choose to ignore the possible higher $q$ values suggested by higher lags that appear significant (look at the 21-27 range on your ACF plot), but it can't hurt to compare these models to the MA(14) for thoroughness. These may just be a product of some seasonality of your model.

In short: Start with choosing the highest significant lag in the initial grouping of your lags, then compare models on a test set.

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