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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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