I am trying to write a mathematical equation for a seasonal ARIMA model of ARIMA (0,0,1)(0,1,1) where the values are recorded quarterly.

I have tried to follow other examples but i cant seem to get my head around these specific examples and cant apply them to my model.

Any help would be greatly appreciated

  • $\begingroup$ Try looking up similar questions here at Cross Validated (see the column on the right or just search relevant keywords), there should be a few that fit your problem closely. $\endgroup$ – Richard Hardy Oct 24 '15 at 11:15
  • $\begingroup$ This question is unanswerable at present. It seems you looked at "other examples", which? Can you link to them? You couldn't "get [your] head around" them, why not? We can answer questions that might otherwise be duplicates if we know what part of the duplicate you didn't understand, otherwise we'd just have to copy the information in toto, which obviously wouldn't help you. $\endgroup$ – gung - Reinstate Monica Oct 24 '15 at 14:28


I took quarterly series (in logs) and estimated your model and obtained enter image description here . I also asked for a pure right hand side ( regression form ) version and obtained enter image description here This second form is usable by "beginners" in time series as it often clears up the fog and aids understanding/comprehension. A third way is to restate the ARIMA model as a PDL/ADL in the history of the series since ARIMA models are simply optimal weighted averages of the past. You can (in this case ) obtain those weights (coefficients of the past) by dividing [1-B4] by [1+.727B1][1-.708**4]. These are called the pi weights enter image description here. Thus the question "How many values should I use in my weighted average and what weights should I apply" is answered by ARIMA.

See Seeking certain type of ARIMA explanation for a more detailed discussion of the equivalence of ARIMA and weighted averages.

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    $\begingroup$ Why not leave a comment linking to your previous answer, or write a new answer with some basic information and a link to it? Copying and pasting your previous answer doesn't seem appropriate. $\endgroup$ – gung - Reinstate Monica Oct 24 '15 at 12:32
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    $\begingroup$ I'm not sure how this addresses the question, isn't the Box and Jenkins airlines data set monthly not quarterly? To the extent that the OP's question is not a duplicate, it requires quarterly data. $\endgroup$ – Silverfish Oct 24 '15 at 12:50
  • $\begingroup$ @silverfish as you correctly said the airline series is monthly but the "message" remains the same for any seasonality. The OP did not specify the seasonality. $\endgroup$ – IrishStat Oct 24 '15 at 14:11
  • $\begingroup$ @silverfish upon closer reading he did ask for quarterly .... One can simply substitute a 4 for my 12 to deal with that. I will edit my answer appropriately. $\endgroup$ – IrishStat Oct 24 '15 at 14:22

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