$216/17$

Many forecasting models use parameters that are estimated using nonlinear optimization. A good example is the Bass model introduced in this chapter. Another example is the exponential smoothing forecasting model, The exponential smoothing model is common in practice, For instance, the basic exponential smoothing model for forecasting sales is

hat$(y{)}_{t+1}=y_t+(1-)hat(y{)}_t$

where

hat$(y{)}_{t+1}=$ foracast $of$ sales for period $t+1$

$y_t=$ actual value $of$ sales for period $t$

hat$(y{)}_t=$ forecast $of$ sales for period $t$

$=$ smoothing constant $0a1.$

This model is used recursively; the forecast for time period $t+1$ is based on the forecast for period $t,$hat$(y{)}_t,$ the observed value of sales in period $t_r{y}_t,$ and the smoothing parameter $.$ The use of this model to forecast sales for $12$ months is illustrated in the table with the smoothing constant $=0\mathrm{.}3.($Note; We are displaying rounded intermediate values for practical purposes. However, the calculations are made using the unrounded values.$)$

Exponential Snoothing Model for $=0\mathrm{.}3$

$\backslash$table$[[\backslash$table$[[$Week$],[(t)$