Question

Q3 A-E

Q3. Based on the time series values from problem number 2, consider the following table of exponential smoothing values using a = 0.3 for the time series. Forecast (F) error Squared error Month Units Sold (Thousands) 9 * 1 2 برا برا 6 6 4 5 (i)? 7.2000 6.8400 6.5880 8.2116 (iii)? (ii)? -1.2000 -0.8400 5.4120 0.7884 36 1.44 0.7056 29.2897 0.6216 12 9 6 7

Answer 1

Month Squared error -6 Unit sold 1 2 3 4 5 6 7 Forecast(t) error 9 - 3 9 6 7.2 6 6.84 12 6.588 9 8.2116 8.44812 -1.2 -0.84 5.412 0.7884 36 1.44 0.7056 29.289744 0.62157456

i) Forecast value of month 2 = Actual value of month 1 =9

ii) error for month 2 = Actual value of month 1-Forecast value of month 2 = 3-9 = -6

iii) Here alpha=0.3

Forecast value of month 7 = 0.3 * actual value of month 6 + (1-0.3) * forecast value of month 6

= 0.3 * 9+ 0.7 *8.2116= 8.44812

iv) Mean squared error = MSE = sum( Squared error)/5

     MSE= (36+1.44+0.7056 +29.2897 + 0.6216)/ 5

           =68.05691856 / 5

           = 13.61138371

V) Compare this MSE with moving average MSE from question 2, and select model with low MSE. That model is better.

( Hope this will help you and like you, if any difficulty feel free to comment. Thank you)