Answer:
Three-week moving average forecast
[tex]\begin{array}{ccc}{Week} & {Time\ Series\ Value} & {Forecast} & {1} & {18} & { } & 2 & {13} & { } & {3} & {16} & { } & {4} & {11} & {15.67 } & 5 & {17} & {13.33 } & {6} & {14} & {14.67 } \ \end{array}[/tex]
[tex]MSE = 11.90[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Month} & {1} & {2} & {3} & {4} & {5}& {6} & {Value} & {18} & {13} & {16} & {11} & {17} & {14} \ \end{array}[/tex]
Solving (a): Three-week moving average forecast
This is calculated as:
[tex]F_{t+1} = \frac{\sum recent\ k\ data}{k}[/tex]
Since it is three-week, we start from t = 3
For t = 3; we consider months 1, 2 and 3
[tex]F_{3+1} = \frac{18 + 13 + 16}{3}[/tex]
[tex]F_{4} = \frac{47}{3}=15.67[/tex]
For t = 4; we consider months 2, 3 and 4
[tex]F_{4+1} = \frac{13 + 16+11}{3}[/tex]
[tex]F_{5} = \frac{40}{3}=13.33[/tex]
For t = 5; we consider months 3, 4 and 5
[tex]F_{5+1} = \frac{16+11+17}{3}[/tex]
[tex]F_{6} = \frac{44}{3}=14.67[/tex]
So, the forecast are:
[tex]F_{4} =15.67[/tex]
[tex]F_{5} = 13.33[/tex]
[tex]F_{6} = 14.67[/tex]
[tex]\begin{array}{ccc}{Week} & {Time\ Series\ Value} & {Forecast} & {1} & {18} & { } & 2 & {13} & { } & {3} & {16} & { } & {4} & {11} & {15.67 } & 5 & {17} & {13.33 } & {6} & {14} & {14.67 } \ \end{array}[/tex]
Solving (b): MSE
To do this, we simply calculate the square of the forecast error
The forecast error (E) is:
[tex]E = Time\ Series\ Value - Forecast[/tex]
So, we have:
Forecast error The square
[tex]E_4 = 11 - 15.67 = -4.67[/tex] [tex]E_4^2 =21.81[/tex]
[tex]E_5 = 17 - 13.33 = 3.67[/tex] [tex]E_5^2 = 13.45[/tex]
[tex]E_6 = 14 - 14.67 = -0.67[/tex] [tex]E_6^2 = 0.45[/tex]
[tex]MSE = \frac{E_4^2 + E_5^2 + E_6^2}{3}[/tex]
[tex]MSE = \frac{21.81 + 13.45 + 0.45}{3}[/tex]
[tex]MSE = \frac{35.71}{3}[/tex]
[tex]MSE = 11.90[/tex]
