1. Two independent forecasting methods have been used each week for the past 5 w
ID: 328599 • Letter: 1
Question
1. Two independent forecasting methods have been used each week for the past 5 weeks. The forecasts and actual sales are as follows.
Week
Actual Sales
(number of units)
Sales Forecasts
(number of units)
Method 1
Method 2
Five weeks ago
20
18
21
Four weeks ago
19
19
20
Three weeks ago
21
20
19
Two weeks ago
18
19
17
Last week
22
23
22
a. Calculate the Mean Absolute Deviation (MAD) measures for forecasting methods 1 and 2. Which forecasting method is better based on MAD?
b. Calculate the Mean Squared Error (MSE) measures for forecasting methods 1 and 2. Which forecasting method is better based on MSE?
c. Calculate the Mean Absolute Percent Error (MAPE) measures for forecasting methods 1 and 2. Which forecasting method is better based on MAPE?
Week
Actual Sales
(number of units)
Sales Forecasts
(number of units)
Method 1
Method 2
Five weeks ago
20
18
21
Four weeks ago
19
19
20
Three weeks ago
21
20
19
Two weeks ago
18
19
17
Last week
22
23
22
Explanation / Answer
To be calculated:
(a) Mean Absolute Deviation (MAD)
(b) Mean Squared Error (MSE)
(c) Mean Absolute Percent Error (MAPE)
Solution:
(a) Mean absolute deviation, MAD is calculated as;
Mean Absolute Deviation (MAD) = Sum of Absolute (Actual values - Forecast Values) / Total number of periods
Method 1
Mean Absolute Deviation (MAD) = Absolute values [(20-18) + (19-19) + (21-20) + (18-19) + (22-23)] / 5
Mean Absolute Deviation (MAD) = (2 + 0 + 1 + 1 + 1) / 5
Mean Absolute Deviation (MAD) = 1
Method 2
Mean Absolute Deviation (MAD) = Absolute values [(20-21) + (19-20) + (21-19) + (18-17) + (22-22)] / 5
Mean Absolute Deviation (MAD) = (1 + 1 + 2 + 1 + 0) / 5
Mean Absolute Deviation (MAD) = 1
On the basis of mean absolute deviation, both methods are same as the values of MAD for both the methods are same.
(b) Mean Squared Error, MSE is calculated as;
MSE = Sum of [Actual values - Forecast Values]^2 / N
Method 1
MSE = [(20-18)^2 + (19-19)^2 + (21-20)^2 + (18-19)^2 + (22-23)^2] / 5
MSE = (4 + 0 + 1 + 1 + 1) / 5
MSE = 1.4
Method 2
MSE = [(20-21)^2 + (19-20)^2 + (21-19)^2 + (18-17)^2 + (22-22)^2] / 5
MSE = (1 + 1 + 4 + 1 + 0) / 5
MSE = 1.4
On the basis of mean squared error, both methods are same as the values of MSE for both the methods are same.
(c) Mean Absolute Percentage Error, MAPE is calculated as;
MAPE = 1/ N x [Sum of absolute values of (Actual - Forecast) / (Actual) ] x 100
Method 1
MAPE = 1/ 5 x Absolute values [(20-18)/20 + (19-19)/19 + (21-20)/21 + (18-19)/18 + (22-23)/22] x 100
MAPE = 1/ 5 x (0.1 + 0 + 0.048 + 0.056 + 0.045) x 100
MAPE = 4.98%
Method 2
MAPE = 1/ 5 x Absolute values [(20-21)/20 + (19-20)/19 + (21-19)/21 + (18-17)/18 + (22-22)/22] x 100
MAPE = 1/ 5 x (0.05 + 0.053 + 0.095 + 0.056 + 0) x 100
MAPE = 5.08%
On the basic of the mean absolute percent error (MAPE), method 1 is better as the value of MAPE is lower for method 1 (4.98%) in compared to method 2 (5.08%). A lower value of MAPE shows that the percentage error between the actual and forecasted values for method 1 is lower than the corresponding values for method 2 and therefore, forecasting Method 1 is more accurate on the basis of MAPE.
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