= Simple exponential smoothing
{title2=$\ell_t=\alpha X_t+(1-\alpha)\ell_{t-1}$}
For $0<\alpha<1$, update a local level by the displayed recursion and forecast every future horizon by $\ell_t$. Iteration gives geometrically decreasing weights $\alpha(1-\alpha)^j$ on past observations and a vanishing contribution from the initial level. It is useful for a locally stable level without a persistent trend or seasonality. A trend causes lag, motivating <double exponential smoothing>.
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