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 $\alpha$ .

$\alpha = 1 - ma_1$