Question

The following time series shows the sales of a particular product over the past 12 months.

Month	Sales
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

Use α = 0.5 to compute the exponential smoothing forecasts for the time series. (Round your answers to two decimal places.)

Month t	Time Series Value Yt	Forecast Ft
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

Use a smoothing constant of α = 0.7 to compute the exponential smoothing forecasts. (Round your answers to two decimal places.)

Month t	Time Series Value Yt	Forecast Ft
1	105
2	135
3	120
4	105
5	90
6	120
7	145
8	140
9	100
10	80
11	100
12	110

Week	Sales (1,000s of gallons)
1	17
2	22
3	19
4	24
5	19
6	16
7	21
8	19
9	23
10	20
11	16
12	22

(a) Compute four-week and five-week moving averages for the time series.

Week	Time Series Value	4-Week Moving Average Forecast	5-Week Moving Average Forecast
1	17
2	22
3	19
4	24
5	19
6	16
7	21
8	19
9	23
10	20
11	16
12	22

Compute the MSE for the four-week moving average forecasts. (Round your answer to two decimal places.)

Compute the MSE for the five-week moving average forecasts. (Round your answer to two decimal places.)

Answer 1

for exponential smoothing: next period forecast =α*last period actual+(1-α)*last period forecast

for alpha =0.5:

week	value	forecast
1	105
2	135	105.00
3	120	120.00
4	105	120.00
5	90	112.50
6	120	101.25
7	145	110.63
8	140	127.81
9	100	133.91
10	80	116.95
11	100	98.48
12	110	99.24

for alphja =0.7:

week	value	forecast
1	105
2	135	105.00
3	120	126.00
4	105	121.80
5	90	110.04
6	120	96.01
7	145	112.80
8	140	135.34
9	100	138.60
10	80	111.58
11	100	89.47
12	110	96.84

2)

a)

			4 period	5 period
week	value		forecast	forecast
1	17
2	22
3	19
4	24
5	19		20.50
6	16		21.00	20.2
7	21		19.50	20
8	19		20.00	19.8
9	23.00		18.75	19.8
10	20.00		19.75	19.6
11	16.00		20.75	19.8
12	22.00		19.50	19.80

MSE for the four-week moving average forecasts =9.68

MSE for the five-week moving average forecasts =6.99