(Solved Homework): Given is a historical time series for job services demand in the prior 6 months. Month Demand…

Given is a historical time series for job services demand in the prior 6 months.

Month Demand
1 11
2 14
3 15
4 14
5 15
6 19

a) The MAD based on the Exponential smoothing α = 0.2 method =  (4 decimal places)

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b) The MAD based on the 3 months moving average method =  (in 4 decimal places)

c) The MSE based on the 3 months moving average method =

d) Use MAD as an criterion to evaluate forecasting methods I (exponential smoothing, α = 0.2 ) and II (3 month moving average). The most accurate forecasting methods between I and II is method  (enter I or II)

Expert Answer


(a) In exponential smoothing we use two terms: At  and  Ft

At is used for Actual Demand

Ft is used for Forecasted Demand

The formula used is Ft+1 = αAt + (1-α)Ft

Substituting α= 0.2 (mentioned in the question)

Ft+1 = 0.2At + 0.8Ft

To calculate F2 we need values of A1 and F1. We have value of A1 but not F1. So we can assume A1 = F1 for calculating values further

Month Demand
1 11
2 14
3 15
4 14
5 15
6 19

F2 = 0.2*A1 + 0.8*F1

F2 = 0.2*11 + 0.8 * 11


F1 and F2 values are same. So, we can safely assume A1 = F2 and calculate further based on this assumption

When calculated using the above mentioned formula, forecasted values are as mentioned below

Month Demand Forecast
1 11
2 14 11
3 15 11.6
4 14 12.28
5 15 12.624
6 19 13.0992

MAD is Mean Absolute Deviation.

Deviation = Actual value – Forecast value

For ex, for month 4 , Deviation = 14 – 12.28 = 1.72

Absolute deviation means absolute value of the deviations calculated

Month Demand Forecast Deviation Absolute deviation
1 11
2 14 11
3 15 11.6 3.4 3.4
4 14 12.28 1.72 1.72
5 15 12.624 2.376 2.376
6 19 13.0992 5.9008 5.9008

MAD is the average of absolute deviations

Since, F2 is based on the assumption, we consider deviations from month 3 for calculating MAD.

MAD = ( 3.4+1.72+2.376+5.9008)/4 = 3.3492

(b) In moving average, demand for current month is forecasted as an average of previous months. So, in a 3 month moving forecast, the fourth month forecast would be the average of demand of first three months. Also, we start forecasting from fourth month because until third month we donot have values to calculate a 3 month moving average.

Once we have forecasted values, MAD is calculated in similar way as mentioned in part (a).

The following table is the result

Month Demand Forecast Deviation Absolute Deviation
1 11
2 14
3 15
4 14 13.3333 0.6667 0.6667
5 15 14.3333 0.6667 0.6667
6 19 14.6667 4.3333 4.3333

MAD =(0.6667+0.6667+4.3333)/3 =1.8889

(c) MSE is the mean square error . It is the average of squares of the errors or deviations.

MSE =( 0.66672 + 0.66672 + 4.33332 )/3 = 6.5556

(d) II since MAD is less

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