I think that there should be slight difference between m1a and m1b due to different initial values. Technically, there should be no difference using the original series and set d=1 (m1a) and using differenced series and set d=0. However, the results are completely different. It looks like m1b is correct. I don't know why. I had the same problem for ARIMA and GARCH. At the end of the day, we need m1a. Usually, we are interested in predicting the original series, e.g. GDP not first-difference GDP.

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1 Answer 1


z1 and dz1 differ by one differencing operation, specifically a seasonal difference. Meanwhile, your model specifications in m1a and m1b differ by two differencing operations, one nonseasonal and one seasonal: you have orders (1,1,0)x(0,1,1) and (1,0,0)x(0,0,1).

To match the two, either difference dz1 once more (non-seasonally) or try (1,1,0)x(0,1,1) and (1,1,0)x(0,0,1).


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