2.2.4.2.2 Algorithm for Single Exponential Smoothing

Single Exponential Model

L_t = \alpha y_t + (1- \alpha)L_{t-1}
\hat{y}_{t+f} = L_{t}
var(\hat{y}_{t+f}) = var(\epsilon_t)(1+(f-1)\alpha^2)
where L_t is the level(mean) component at time t. The parameter \alpha controls the weight of smoothing. y_t and \hat{y_t} are data value and fitted value at time t.var(\epsilon_t) is estimated as the mean deviation.

Weights by Optimal ARIMA

Use an ARIMA (0,1,1) model to fit the data. With the parameters ma_1, calcualte \alpha .

\alpha = 1 - ma_1