Question

Develop the three-week moving average forecasts for this time series. (Round your answers to two decimal places.)WeekTime SeriesValueForecast118211316410 Incorrect: Your answer is incorrect.517 Incorrect: Your answer is incorrect.615 Incorrect: Your answer is incorrect.Compute MSE. (Round your answer to two decimal places.)MSE

Answer 1

Three-week moving average forecast

`\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}`

`MSE = 11.90`

Explanation:

Given

`\begin{array}{ccccccc}{Month} & {1} & {2} & {3} & {4} & {5}& {6} & {Value} & {18} & {13} & {16} & {11} & {17} & {14} \ \end{array}`

Solving (a): Three-week moving average forecast

This is calculated as:

`F_(t+1) = (\sum recent\ k\ data)/(k)`

Since it is three-week, we start from t = 3

For t = 3; we consider months 1, 2 and 3

`F_(3+1) = (18 + 13 + 16)/(3)`

`F_(4) = (47)/(3)=15.67`

For t = 4; we consider months 2, 3 and 4

`F_(4+1) = (13 + 16+11)/(3)`

`F_(5) = (40)/(3)=13.33`

For t = 5; we consider months 3, 4 and 5

`F_(5+1) = (16+11+17)/(3)`

`F_(6) = (44)/(3)=14.67`

So, the forecast are:

`F_(4) =15.67`

`F_(5) = 13.33`

`F_(6) = 14.67`

`\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}`

Solving (b): MSE

To do this, we simply calculate the square of the forecast error

The forecast error (E) is:

`E = Time\ Series\ Value - Forecast`

So, we have:

Forecast error The square

`E_4 = 11 - 15.67 = -4.67`
`E_4^2 =21.81`

`E_5 = 17 - 13.33 = 3.67`
`E_5^2 = 13.45`

`E_6 = 14 - 14.67 = -0.67`
`E_6^2 = 0.45`

`MSE = (E_4^2 + E_5^2 + E_6^2)/(3)`

`MSE = (21.81 + 13.45 + 0.45)/(3)`

`MSE = (35.71)/(3)`

`MSE = 11.90`