Question

The U.S. Census Bureau publishes data on factory orders for all manufacturing, durable goods, and nondurable goods industries. Shown below are factory orders in the United States over a 13- year period ($ billion). First, use the data to develop forecasts for years 6 through 13 using a 5-year moving average. Then, use the data to develop forecasts for years 6 through 13 using a 5-year weighted moving average. Weight the most recent year by 6, the previous year by 4, the year before that by 2, and the other years by 1. Answer the following questions: a) What is the forecast for year 13 based on the 5-year moving average? b) What is the forecast for year 13 based on the 5-year weighted moving average? c) What is the MAD for the moving average forecast? d) What is the MAD for the weighted moving average forecast? e) Which forecasting model is better? Year Factory orders 1 2,512.70 2 2,739.20 3 2,874.90 4 2,934.10 5 2,865.70 6 2,978.50 7 3,092.40 8 3,052.60 9 3,145.20 10 3,114.10 11 3,257.40 12 3,654.00 13

Answer 1

a)

period	value	Forecast	|error|
1	2512.7
2	2739.2
3	2874.9
4	2934.1
5	2865.7
6	2978.5	2785.32	193.18
7	3092.4	2878.48	213.92
8	3052.6	2949.12	103.48
9	3145.2	2984.66	160.54
10	3114.1	3026.88	87.22
11	3257.4	3076.56	180.84
12	3654	3132.34	521.66
13		3244.66
		average	208.69

from above: forecast for year 13 based on the 5-year moving average =3244.66

b)

period	value	Forecast	|error|
1	2512.7
2	2739.2
3	2874.9
4	2934.1
5	2865.7
6	2978.5	2852.31	126.19
7	3092.4	2915.44	176.96
8	3052.6	3000.63	51.97
9	3145.2	3031.57	113.63
10	3114.1	3079.33	34.77
11	3257.4	3102.96	154.44
12	3654	3174.01	479.99
13		3384.26
		average	162.56

forecast for year 13 based on the 5-year weighted moving average =3384.26

c)

MAD for the moving average forecast =208.69

d)

MAD for the weighted moving average forecast =162.56

e)

e weighted moving average forecast is better because of lower MSE