Two different forecasting techniques were used to forecast demand for cases of bottled water in a store. Actual demand and the two sets of forecasts for seven periods are as follows:

Forecast Demand

Period Demand F$1$ F$2$

$1666969$

$2757072$

$3697070$

$4717168$

$5687171$

$6717269$

$7747271$

a$-1.$ Calculate the MAD for each set of forecasts. $($Round the final answers to $2$ decimal places.$)$

F$1$

F$2$

a$-2.$ Which technique appears to be more accurate?

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b$-1.$ Calculate the MSE for each set of forecasts. $($Round the final answers to $2$ decimal places.$)$

F$1$

F$2$

b$-2.$ Which technique appears to be more accurate?

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c$-1.$ Calculate the MAPE for each set of forecasts. $($Round the final answers to $2$ decimal places.$)$

F$1$

$\%$

F$2$

$\%$

c$-2.$ Which technique appears to be more accurate?

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d$-1.$ Do all three of forecast errors provide the same conclusion $($i$.$e$.,$ are they consistent$)$ in this case?

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d$-2.$ Do you expect consistent results in every case?

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$,$

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will have lower MSE than

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if obs $7$ for F$1$ was $77.$

e$.$ In practice, either MAD, MSE, or MAPE would be employed to compute a measure of forecast errors. What factors might lead a manager to favour one?

MAD

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MSE

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MAPE

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