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 \(\alpha\) .

\[\alpha = 1 - ma_1\]