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.