The past monthly demands are shown below. The naïve method, that is, the one-period moving average method, is applied to make forecasts. What is the mean square error of the forecasts?
A) −1.67
B) 275.00
C) 91.67
D) 8.33

Question

The past monthly demands are shown below. The naïve method, that is, the one-period moving average method, is applied to make forecasts.  What is the mean square error of the forecasts?
A) −1.67 
B) 275.00 
C) 91.67 
D) 8.33

Quizplus · Accepted Answer

To calculate the mean square error (MSE), we first need to find the errors (the difference between the forecast and the actual demand). Using the naïve method (one-period moving average method), the forecast for each month is equal to the actual demand for the previous month. Therefore, we can calculate the errors as follows:

Error for Jan = Actual demand for Jan - Forecast for Jan = 80 - 75 = 5
Error for Feb = Actual demand for Feb - Forecast for Feb = 95 - 80 = 15
Error for Mar = Actual demand for Mar - Forecast for Mar = 100 - 95 = 5
Error for Apr = Actual demand for Apr - Forecast for Apr = 105 - 100 = 5

To calculate the MSE, we need to square each error, then take the average of the squared errors. Therefore, we have:

MSE = ((5^2) + (15^2) + (5^2) + (5^2))/4 = 91.67

Therefore, the best choice is C.

The Past Monthly Demands Are Shown Below