Question

2.   Calculate Mean Absolute Error ( MAD) for the data in question 1 for the three     methods used. Round MAD to two decimal places. ( 4 marks)

Year	Revenue	4-Year Moving Average	Absolute Error	4 Weighted Moving Average Weights 4,3,2,1	Absolute Error	Exponential    Smoothing          α = 0.6	Absolute Error
2010	75
2011	81
2012	74
2013	79
2014	69
2015	92
2016	73
2017	85
2018	90
2019	73
2020 Forecast

What does MAD measures? which of these three forecasting methods provides better forecast of the revenue data ? ( 2 mark)

Answer 1

The formulas for the three methods are:

a) 4-year moving average:

Ft = (At-1 + At-2 + At-3 + At-4)/4

b) Weighted moving average:

Ft = (4*At-1 + 3*At-2 + 2*At-3 + 1*At-4)/10

c) Exponential smoothing:

Ft = 0.6*At-1 + 0.4*Ft-1

The calculations for the three methods are given below:

Year	Revenue	4-Year Moving Average	Absolute Error	4 weighted moving average (Weights 4,3,2,1)	Absolute Error	Exponential smoothing (alpha = 0.6)	Absolute error
2010	75					75.00	0.00
2011	81					75.00	6.00
2012	74					78.60	4.60
2013	79					75.84	3.16
2014	69	77.25	8.25	77.5	8.50	77.74	8.74
2015	92	75.75	16.25	74.2	17.80	72.49	19.51
2016	73	78.5	5.5	80.7	7.70	84.20	11.20
2017	85	78.25	6.75	78.5	6.50	77.48	7.52
2018	90	79.75	10.25	81.2	8.80	81.99	8.01
2019	73	85	12	85.3	12.30	86.80	13.80
2020 (Forecast)		80.25		80.5		78.52	78.52
Mean Absolute Deviation			9.83		10.27		8.25

Mean absolute deviation (MAD) measures the mean deviation of the forecasted values from the actual values which is a measure of the accuracy of the forecasting method.

MAD for each of the method is given. Out of the three forecasting methods, exponential smoothing with alpha = 0.6 has the lowest MAD value of 8.25. Hence, it provides a better forecast of the revenue data, Forecast (2020) = 78.52