Question

Measuring the forecast accuracy of the na¨ıve method. consider the following time series data: week 1 2 3 4 5 6 value 18 13 16 11 17 14 using the na¨ıve method (most recent value) as the forecast for the next week, compute the following:

a) mean absolute error
b) mean squared error
c) mean absolute percentage error
d) forecast for week 7

Answer 1

To measure the forecast accuracy of the naïve method, we calculate the mean absolute error (MAE), mean squared error (MSE), mean absolute percentage error (MAPE), and forecast for week 7 using the given time series data.

Step-by-step explanation:

To measure the forecast accuracy of the naïve method, we need to calculate the following:

a) Mean Absolute Error (MAE): The MAE is the average of the absolute errors. We find the absolute error by subtracting the actual value from the forecasted value for each week, and then take the average of these errors.
MAE = (|18 - 13| + |13 - 16| + |16 - 11| + |11 - 17| + |17 - 14|) / 5

b) Mean Squared Error (MSE): The MSE is the average of the squared errors. We square the error for each week, find the average, and then take the square root to get the MSE.
MSE = ((18 - 13)^2 + (13 - 16)^2 + (16 - 11)^2 + (11 - 17)^2 + (17 - 14)^2) / 5

c) Mean Absolute Percentage Error (MAPE): The MAPE measures the percentage difference between the forecasted value and the actual value. We find the absolute percentage error for each week, take the average, and multiply by 100 to get the percentage.
MAPE = ((|18 - 13| / 18) + (|13 - 16| / 13) + (|16 - 11| / 16) + (|11 - 17| / 11) + (|17 - 14| / 17)) / 5 * 100

d) Forecast for Week 7: The forecast for week 7 using the naïve method is equal to the most recent value, which is 14.