A jeweler wants to forecast sales of onecarat diamond rings

A jeweler wants to forecast sales of one-carat diamond rings. sales data for the previous 15 weeks have been obtained: Develop a series of forecasts, beginning in week 4, that would have resulted if a three-period moving average forecast had been used. using a starting forecast for week 4 of 23 rings, develop the forecasts that would have resulted if an exponential smoothing model with alpha = .20 had been used.

Solution

a. 3 period moving forecast beginning week 4 will involve week 1, 2, 3. This will give the forecast for week 4 i.e the moving averages of week 1,2,3 will be the forecast figure for week 4.

b. formula:

Forecast (m) for week 4 = 23.

m (forecast) for week 5 = alpha*actuals for week 5+(1-alpha)*forecast for week 4

Week	Sales	3 period moving total	3 period moving average	Forecast
1	25
2	19
3	24	68	22.67
4	28	71	23.67	22.67
5	30	82	27.33	23.67
6	35	93	31.00	27.33
7	32	97	32.33	31.00
8	36	103	34.33	32.33
9	34	102	34.00	34.33
10	30	100	33.33	34.00
11	32	96	32.00	33.33
12	25	87	29.00	32.00
13	29	86	28.67	29.00
14	32	86	28.67	28.67
15	30	91	30.33	28.67
				30.33