Question

1. Moving Averages.  Use the below actual sales to calculate a three-year average which will be used as the forecast for next periods (chapter 14, text).
2. Exponential Smoothing. Use the same data to forecast sales for the next periods with α=.40 (chapter 14, text)

Month	Actual Sales
1	3050
2	2980
3	3670
4	2910
5	3340
6	4060
7	4750
8	5510
9	5280
10	5504
11	5810
12	6100

Answer 1

3 year moving average forecast:

Month	Actual Sales	3 months moving total	3 months moving average	3 months moving forecast
1	3,050.00
2	2,980.00
3	3,670.00	9,700.00	3,233.33
4	2,910.00	9,560.00	3,186.67	3,233.33
5	3,340.00	9,920.00	3,306.67	3,186.67
6	4,060.00	10,310.00	3,436.67	3,306.67
7	4,750.00	12,150.00	4,050.00	3,436.67
8	5,510.00	14,320.00	4,773.33	4,050.00
9	5,280.00	15,540.00	5,180.00	4,773.33
10	5,504.00	16,294.00	5,431.33	5,180.00
11	5,810.00	16,594.00	5,531.33	5,431.33
12	6,100.00	17,414.00	5,804.67	5,531.33
13				5,804.67

Thus forecast for the 13th month will be = 5,804.67

Exponential smoothing:

Here new forecast = last period's forecast + alpha*(last period's actual figure - last period's forecast)

Forecast for January will be assumed as 3,050. Thus:

Month	Actual Sales	Forecast
1	3,050.00	3,050.00
2	2,980.00	3,050.00
3	3,670.00	3,022.00
4	2,910.00	3,281.20
5	3,340.00	3,132.72
6	4,060.00	3,215.63
7	4,750.00	3,553.38
8	5,510.00	4,032.03
9	5,280.00	4,623.22
10	5,504.00	4,885.93
11	5,810.00	5,133.16
12	6,100.00	5,403.89
13		5,682.34

Thus forecast for 13th month = 5,682.34