Question

Q3. error 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. Units Sold Forecast (F) Squared error Month (Thousands) 9 2 3 (0)? (ii)? 36 3 6 7.2000 -1.2000 1.44 4 6 6.8400 -0.8400 0.7056 5 12 6.5880 5.4120 29.2897 6 9 8.2116 0.7884 0.6216 7 (iii)? a) (3pt) Compute the number (i): Show your work for full credit b) (3pt) Compute the number (ii): Show your work for full credit c) (5pt) Compute the number (iii): Show your work for full credit d) (6pt) What is the mean square error (MSE)? Show your work for full credit e) (6pt) Compare the MSE for part (Q3.d) using exponential smoothing values and (Q2.e) using the 3-month moving average. Which method is better and why?

Answer 1

The necessary calculations done below.

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

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

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

c) 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

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

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

           =68.05691856 / 5

           = 13.6114

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

The Calculation for MSE is,

Month Unit sold 1 2. 3 4 5 6 7 3 month moving average Squared Error 9 3 6 6 6 0 12 5 49. 9 8 1 9

MSE for 3month moving average= sum( squared error) / 3 = (0+49+1)/3 = 16.67

from d) MSE for exponential smoothing model= 13.6114

Here MSE for exponential smoothing (13.6114) < MSE for 3month moving average = (16.67), therefore we can say that the exponetial smoothing is better than the 3 month moving average.

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