Question

Ms. Kathleen Boyd, director of logistics for the Scenic Calendar Company, wishes to evaluate

two methods of time series forecasting. She has collected quarterly calendar sales data from the

years 2003 and 2004.

2003 . 2004

Qtr. Actual Sales Qtr. Actual Sales

1 1200 1 1300

2 800 2 800

3 200 3 250

4 1000 4 1200

a.Use the moving averages technique to find forecasted sales for the third quarter of 2009 based on actual sales from the previous three quarters. (0,5p)

b. Use simple exponential smoothing to forecast each quarter’s sales in 2009, given that Mr. Clayton qualitatively forecasted 800 calendars for quarter 4, 2008. Mr. Clayton has assigned an alpha factor of 0,1 for time series sensitivity. (0,5p)

c. Repeat the simple exponential smoothing problem above (part 5b) with Mr Clayton employing an alpha factor of 0,8. (0,5p)

d. How well does the moving averages and simple exponential smoothing techniques seem to work in Mr. Clayton’s situation? In what ways do the techniques appear to fail? Explain. (0,5p)

Answer 1

a. If Growth of Sales Remains Constant then

Average=Sum of All Quaters/4

	2003	2004	2005	2006	2007	2008	2009
Quarter 1	1200	1,300	1,400	1500	1600	1700	1800
Quarter 2	800	800	800	800	800	800	800
Quarter 3	200	250	300	350	400	450	1350
Quarter 4	1,000	1,200	1,400	1,600	1,800	2,000	2,200
Average	800	888	975	1062.5	1,150	1,238	1,325

Sales of 3rd Quater of 2009

(1800+2000)/2=1900

(1900+800)/2=1350.

b.St=axt-1+(1-a)t-1

Alpha is 0

=800(0)+1-0

=1

or

Alpha Is 1

800(1)+1-1

=800

If Alpha is 0.8

=800(0.8)+1-0.8

=640.2

d. Exponential Smoothing Is Inaccurate in Claytons Situations as based on constant growth across all quaters and years is 500 for 3rd Quater of 2009.and Exponential Smoothing provides figures of 1,800,640.2.Moving Average Shows A Value of 1350 instead of 500.

Moving Average and Exponential Smoothing Fail in the following Situations-

a.Exponential Smoothing Fails if Alpha Is Close to 0.

b.Moving Average Doesn't Take into Account Seasonal variations,