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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...

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Statistics

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

MonthSales
1105
2135
3120
4105
590
6120
7145
8140
9100
1080
11100
12110

Use α = 0.5 to compute the exponential smoothingforecasts for the time series. (Round your answers to two decimalplaces.)

Month tTime Series Value

Yt

Forecast

Ft

1105
2135
3120
4105
590
6120
7145
8140
9100
1080
11100
12110

Use a smoothing constant of α = 0.7 to compute theexponential smoothing forecasts. (Round your answers to two decimalplaces.)

Month tTime Series Value

Yt

Forecast

Ft

1105
2135
3120
4105
590
6120
7145
8140
9100
1080
11100
12110
WeekSales (1,000s
of gallons)
117
222
319
424
519
616
721
819
923
1020
1116
1222

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

WeekTime Series
Value		4-Week
Moving
Average
Forecast		5-Week
Moving
Average
Forecast
117
222
319
424
519
616
721
819
923
1020
1116
1222

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 & Explanation Solved by verified expert
4.2 Ratings (706 Votes)

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
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