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Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 17 12 17 15 a. develop the three-week moving average forecasts for this time series....

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Statistics

Consider the following time series data.

Week123456
Value181317121715

a. develop the three-week moving average forecasts for this timeseries. Compute MSE and a forecast for week 7 (to 2 decimals ifnecessary).

b. use = 0.2 to compute the exponential smoothing forecasts forthe time series. Compute MSE and a forecast for week 7 (to 2decimals).

c. use a smoothing constant of =0.4 to compute the MSE (to 2decimals).

Answer & Explanation Solved by verified expert
4.3 Ratings (733 Votes)

a)

Time period Actual Value(A) Moving avg. Forecast(F) Forecast error E=|A-F| Squared Forecast Error
1 18
2 13
3 17
4 12 16.00 4.00 16.00
5 17 14.00 3.00 9.00
6 15 15.33 0.33 0.11
Total 7.33 25.11
Average 2.44 8.37
MAD MSE
MSE = 8.37
forecast for week 7 = 14.67

b)

for exponential smoothing: next period forecast =α*last period actual+(1-α)*last period forecast
Time period Actual Value(A) Forecast(F) Forecast error E=A-F Squared Forecast Error
1 18
2 13 18.00 5.00 25.00
3 17 17.00 0.00 0.00
4 12 17.00 5.00 25.00
5 17 16.00 1.00 1.00
6 15 16.20 1.20 1.44
Total 12.20 52.44
Average 2.44 10.49
MAD MSE
MSE = 10.49
forecast for week 7 = 15.96

c)

Time period Actual Value(A) Forecast(F) Forecast error E=A-F Squared Forecast Error
1 18
2 13 18.00 5.00 25.00
3 17 16.00 1.00 1.00
4 12 16.40 4.40 19.36
5 17 14.64 2.36 5.57
6 15 15.58 0.58 0.34
Total 13.34 51.27
Average 2.67 10.25
MAD MSE
MSE = 10.25
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