Question

Problem 15-01 (Algorithmic)

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	14	15	11	19	14

Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy.

1. Mean absolute error. Round your answer to one decimal place.
   
   
   
2. Mean squared error. Round your answer to one decimal place.
   
   
   
3. Mean absolute percentage error. Round your answer to two decimal places.
   
   
   
4. What is the forecast for week 7? Round your answer to the nearest whole number.
   

Answer 1

Solution:

Naive method: In naive forecast method (most recent value), the forecast for the next week is simply the actual value of the current week. Using the naive method, the forecast for the given weeks is calculated as below:

Forecast for week 2 = Actual value of week 1 = 18

Forecast for week 3 = Actual value of week 2 = 14

Forecast for week 4 = Actual value of week 3 = 15

Forecast for week 5 = Actual value of week 4 = 11

Forecast for week 6 = Actual value of week 5 = 19

(a) Mean Absolute Error (MAE):

MAE = Sum of absolute values of (Actual value - Forecast value) / Number of weeks

MAE = Absolute values of [(14 - 18) + (15 - 14) + (11 - 15) + (19 - 11) + (14 - 19)] / 5

MAE = (4 + 1 + 4 + 8 + 5) / 5

Mean Absolute Error = 4.4

(b) Mean Squared Error (MSE):

MSE = [(Actual value - Forecast value)^2] / Number of weeks

MSE = [(14 - 18)^2 + (15 - 14)^2 + (11 - 15)^2 + (19 - 11)^2 + (14 - 19)^2] / 5

MSE = (16 + 1 + 16 + 64 + 25) / 5

Mean Squared Error = 24.4

(c) Mean Absolute Percentage Error (MAPE):

MAPE = 1/Number of periods x Sum of absolute values of [(Actual - Forecast) / Actual] x 100

MAPE = 1/5 x Absolute values of [(14 - 18)/14 + (15 - 14)/15 + (11 - 15)/11 + (19 - 11)/19 + (14 - 19)/14] x 100

MAPE = 1/5 x (0.29 + 0.07 + 0.36 + 0.42 + 0.36) x 100

MAPE = 1/5 x 150

Mean Absolute Percentage Error = 30.00%

(d) Forecast for week 7:

Forecast for week 7 = Actual value of week 6

Forecast for week 7 = 14