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I am trying to understand how to write a SARIMA equation in a way that is more easily understood, for me. The only specification I can find for the model looks like:

$(1-\phi_1)(1-\Phi_1^4)(1-B)(1-B^4)y_t = (1+\theta_1B)(1+\Theta_1B^4)\epsilon_t$,

for a SARIMA(1,1,1)(1,1,1)4 model. My preferred way of writing these equations are like:

$y_t = \beta_0 + \beta_1 y_{t-1} + \beta_2 y_{t-2} + \beta_3 y_{t-3} + \varepsilon_t$

Here for an AR(3) model. My question is, how would this first equation look if it was written in the same way as the second equation?

Thank you.

Simon Rydstedt
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  • See https://online.stat.psu.edu/stat510/lesson/4/4.1/#paragraph--292 for an example of how to convert the model parameters into an equation of the form you require. Hint: Simple polynomial multiplication. – vvg Jan 04 '23 at 02:26
  • Explain "who is" SARIMA or at least give a reference. – Jean Marie Jan 04 '23 at 09:26
  • No answer to my comment. Do you really believe that this acronym is well known ? – Jean Marie Jan 04 '23 at 22:02
  • Hi, didn't have time to check my notifications. In my world I thought this was well not among mathematicians, but I guess I was wrong. @vvg solved my problem though, wish it would have been an answer so I could accept it as the solution. – Simon Rydstedt Jan 06 '23 at 06:40
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    @JeanMarie: ARIMA is Autoregressive Integrated Moving Average model used in timeseries forecasting. SARIMA is a variant that includes seasonal parametrization. – vvg Jan 06 '23 at 11:36
  • @vvg Thanks. You at least give an answer. – Jean Marie Jan 06 '23 at 12:06
  • @JeanMarie You could have just clicked the link from vvg or made a five sec googling, which I assumed you had already done. Of course it would've been better if I provided an explanation but it isn't even necessary to answer the question. – Simon Rydstedt Jan 06 '23 at 17:41
  • I could have done that... but take the habit to have self-contained information. This is a necessity in particular when you write articles . Don't await the world to know all the acrononyms... – Jean Marie Jan 06 '23 at 18:10
  • This is not an article. It is an question about an equation, where the acronym isn't even necessary to answer the question, and where someone already gave an answer. Excuse me if I get grumpy but it doesn't make sense to make this comparison and you are wasting both of our time. – Simon Rydstedt Jan 06 '23 at 18:15

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