Simple exponential smoothing (${\ell }_t=\alpha X_t+(1-\alpha ){\ell }_{t-1}$)

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.