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?

Answer 1

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.