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I run auto_arima model with seasonality from pmdarima python package. The output summary is the following: table

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 $Θ$

Bruh
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