Consider the following time series data:
Using the naïve method (most recent value) as the forecast for the next week, compute the following measures of forecast accuracy:
- a.
Mean absolute error - b. Mean squared error
- c. Mean absolute percentage error
- d. What is the forecast for week 7?
(a)
Find the value of mean absolute error.
Answer to Problem 1P
The mean absolute error is 4.4.
Explanation of Solution
Week | Time Series Value | Forecast | Forecast Error | Absolute Value of Forecast Error |
1 | 18 | |||
2 | 13 | 18 | −5 | 5 |
3 | 16 | 13 | 3 | 3 |
4 | 11 | 16 | −5 | 5 |
5 | 17 | 11 | 6 | 6 |
6 | 14 | 17 | −3 | 3 |
Total | 22 |
Thus, the mean absolute error is 4.4.
(b)
Obtain the mean squared error.
Answer to Problem 1P
The mean squared error is 20.8.
Explanation of Solution
The mean squared error is obtained as given below:
Absolute Value of Forecast Error | Squared Forecast Error |
5 | 25 |
3 | 9 |
5 | 25 |
6 | 36 |
3 | 9 |
22 | 104 |
Thus, the mean squared error is 20.8.
(c)
Find the mean absolute percentage error.
Answer to Problem 1P
The mean absolute percentage error is 31.88.
Explanation of Solution
The mean absolute percentage error is obtained is given below:
Week | Time Series Value | Forecast | Forecast Error | Percentage Error | Absolute percentage Error |
1 | 18 | ||||
2 | 13 | 18 | −5 | −38.46 | 38.46 |
3 | 16 | 13 | 3 | 18.75 | 18.75 |
4 | 11 | 16 | −5 | −45.45 | 45.45 |
5 | 17 | 11 | 6 | 35.29 | 35.29 |
6 | 14 | 17 | −3 | −21.43 | 21.43 |
Total | −51.30 | 159.38 |
Thus, the mean absolute percentage error is 31.88.
(d)
Obtain the forecast for week 7.
Answer to Problem 1P
The forecast for week 7 is 14.
Explanation of Solution
The forecast for week 7 is obtained as given below:
Thus, the forecast for week 7 is 14.
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