Question

In: Statistics and Probability

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13...

Consider the following time series data.

Week 1 2 3 4 5 6
Value 18 13 16 11 17 14

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

(___)

2.Consider the following time series data.

Week 1 2 3 4 5 6
Value 19 13 17 12 17 15

b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week 7 (to 2 decimals if necessary).

MSE (___)
The forecast for week 7 (___)

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

MSE (___)
The forecast for week 7 (___)

e. Use a smoothing constant of a = 0.4 to compute the MSE (to 2 decimals).

(___)

Solutions

Expert Solution

1)

a)

Period Data ES(0.4) Forecasts
1 18 18
2 13 18+0.4⋅(18−18)=18
3 16 18+0.4⋅(13−18)=16
4 11 16+0.4⋅(16−16)=16
5 17 16+0.4⋅(11−16)=144
6 14 14+0.4⋅(17−14)=15.2
7 - 15.2+0.4⋅(14−15.2)=14.72

2)

b)

Period Data MA(3) Forecasts
1 19 -
2 13 -
3 17 -
4 12 (19 + 13 + 17)/3 = 16.3333
5 17 (13 + 17 + 12)/3 = 14
6 15 (17 + 12 + 17)/3 = 15.3333
7 - (12 + 17 + 15)/3 = 14.6667

fore cast for week 7 = 14.6667

the mean square error is MSE=9.3

c)

MSE 11.88
The forecast for week 7 16.2877

e)


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