I run auto_arima
model with seasonality from pmdarima
python package.
The output summary is the following:
Shortly, it says that the best model is $ARIMA(3,1,2)(0,1,1)_{12}$ with intercept.
Now, I want to write the equation for my model, but I'm not sure that I did it correctly.
Please check it out:
$$ \Delta y_t = 0.618 y_{t-1} - 0.2979 y_{t-2} - 0.4196 y_{t-3} -0.3204 \epsilon_{t-1} -0.5838 \epsilon_{t-2} + \epsilon_{t} -0.4687 \epsilon_{t-12} + 0.0098$$
Edit
Please write it not in terms of $Y_t , e_t, θ$ and $Θ$