(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

Answer

(a) In exponential smoothing we use two terms: A_t and F_t

A_t is used for Actual Demand

F_t is used for Forecasted Demand

The formula used is F_t+1 = αA_t + (1-α)F_t

Substituting α= 0.2 (mentioned in the question)

F_t+1 = 0.2A_t + 0.8F_t

To calculate F₂ we need values of A₁ and F₁. We have value of A₁ but not F_1. 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

=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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