8.1 Local level model, ETS(M,N,N)

Another model that underlies the SES method is ETS(M,N,N), which is formulated as: \[\begin{equation} \begin{split} y_{t} &= l_{t-1}(1 + \epsilon_t) \\ l_t &= l_{t-1} (1 + \alpha \epsilon_t) \end{split} . \tag{5.8} \end{equation}\] Note that in this model it is typically assumed that the mean of error term \(\epsilon_t\) is equal to zero. The model has similar properties to (5.3), but will have increasing variability with the increase of level due to the multiplication in the formula. The smoothing parameter