The Exponential Smoothing Model Is Given By $\hat{y}_{t+1}=\alpha y_{t}+(1-\alpha) \hat{y}_{t}$

question 16

Essay

The exponential smoothing model is given by,
$\hat{y}_{t+1}=\alpha y_{t}+(1-\alpha) \hat{y}_{t}$

where

$\hat{y}$ _(t+1)=forecast of sales for period t+1
y_t=actual sales for period t
$\hat{y}_{t}$ =forecast of sales for period t
α=smoothing constant,0 ≤ α≤1
This model is used to predict the future based on the past data values.
a. The observed values with the smoothing constant α = 0.45 are given in the below table. The third column of the table displays the forecast values obtained using the above model. The forecasted error y_t- (y_t ) ̂ is calculated in the fourth column, and the square of the forecast error and the sum of squared forecast errors are given in fifth column. Construct this table in your spreadsheet model using the formula above. (Hint: The first forecast value is same as the observed value.)
Alpha = 0.45

b. The value of α is often chosen by minimizing the sum of squared forecast errors. Use Excel Solver to find the value of α that minimizes the sum of squared forecast errors.

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