I have a question regarding the difference operator of SARIMA models. I am attempting to write out $SARIMA(2,1,2)(2,1,1)_{24}$. This seasonal ARIMA model has therefore 2 difference operators.
I have tried to follow various different posts on here ... especially this one:
How To Write Seasonal ARIMA model mathematically
However, I am in doubt whether this is actually done correctly. Currently I have the following:
$\nabla^1_{24}\nabla^1X_t$ = $\nabla^1_{24}(X_t-X_{t-1})$ = $X_t-X_{t-1}-X_{t-24}$
Perhaps there is an equation which explains it in more detail (step-wise)?
Thank you in advance.
