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OK, so then this algorithm would not consider that a single ar(4) could be better than ar(1), or ar(1) ar(2) ar(3) ar(4)?

You write: "Automatic arima does not consider seasonal differencing." Instead of using our variable y, would it be possible to just create a LHS variable that is d12y (that is e.g., series d12y=y-y(-12) ), and then use our seasonally differenced d12y in this automatic arima routine in EVie...