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I'd like to represent the order of the Seasonal ARIMA(1,0,0)(1,0,1)60 model mathematically. Here is the equation I came up with so far:

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Eventually, i'd like to represent it as a "conventional" regression equation such:

enter image description here

Can someone tell me if my equations are correct?

Thanks!

Apython
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    It seems correct, you did the product of the polynomials in the left-hand-side and moved the terms to the right-hand-side. Just a couple of things: the constant $c$ does not show up in the first equation and $\Phi_1$ is denoted as $\Phi$. – javlacalle Dec 01 '14 at 00:00
  • Thank you for your replay! can you please tell me why the constant c is being omitted? and explain why Φ cannot be represented as Φ1? what if you have more than 1 seasonal AR estimators? wouldn't it be then necessary to distinguish between them? – Apython Dec 01 '14 at 00:05
  • Can you rephrase your question in such a way that they invite explanation of something rather than a yes or no answer? – Glen_b Dec 01 '14 at 02:46
  • I'm trying to use the order of ARIMA models (100)(101)60 for point forecasts. But rather than just apply the ```auto.arima()``` and ```forecast()``` in R, I'd like to demonstrate it by hand calculations. The problem is that my prediction results were different than the results obtained in R (3.1.1). Therefore, I was wondering if the equations I used were correct or not.. – Apython Dec 01 '14 at 04:17
  • I didn't mean that $\Phi$ cannot be represented as $\Phi_1$, I just pointed it as a possible typo. Similar for the constant $c$. Which results couldn't you replicate? parameter estimates, fitted values, forecasts,...? As in other comment above, I recommend you to give more details in your question. – javlacalle Dec 01 '14 at 08:55

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