1 Consider the following time series data Week Value 2 4 18

1. Consider the following time series data Week Value 2 4 18 13 16 17 14 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? 2. Refer to the time series data in Exercise 1. Using the average of all the historical data as a forecast for the next period, compute the following measures of forecast accuracy: a. Mean absolute error b. Mean squared error

Solution

Sol)

1)

The following table shows the calculations for parts (a), (b), and (c).

Week

Time Series Value

Forecast

Forecast Error

Absolute Value of Forecast Error

Squared Forecast Error

Percentage Error

Absolute Value of Percentage Error

1

18

2

13

18

-5

5

25

-38.46

38.46

3

16

13

3

3

9

18.75

18.75

4

11

16

-5

5

25

-45.45

45.45

5

17

11

6

6

36

35.29

35.29

6

14

17

-3

3

    9

-21.43

21.43

Totals

22

104

-51.30

159.38

        a.     MAE = 22/5 = 4.4

        b.     MSE = 104/5 = 20.8

        c.     MAPE = 159.38/5 = 31.88

        d.     Forecast for week 7 is 14

2)

Week

Time Series Value

Forecast

Forecast Error

Absolute Value of Forecast Error

Squared Forecast Error

Percentage Error

Absolute Value of Percentage Error

1

18

2

13

18.00

-5.00

5.00

25.00

-38.46

38.46

3

16

15.50

0.50

0.50

0.25

3.13

3.13

4

11

15.67

-4.67

4.67

21.81

-42.45

42.45

5

17

14.50

2.50

2.50

6.25

14.71

14.71

6

14

15.00

-1.00

1.00

1.00

-7.14

    7.14

Totals

13.67

54.31

-70.21

105.86

        a.     MAE = 13.67/5 = 2.73

        b.     MSE = 54.31/5 = 10.86

        c.     MAPE = 105.89/5 = 21.18

        d.     Forecast for week 7 is (18 + 13 + 16 + 11 + 17 + 14) / 6 = 14.83

Week	Time Series Value	Forecast	Forecast Error	Absolute Value of Forecast Error	Squared Forecast Error	Percentage Error	Absolute Value of Percentage Error
1	18
2	13	18	-5	5	25	-38.46	38.46
3	16	13	3	3	9	18.75	18.75
4	11	16	-5	5	25	-45.45	45.45
5	17	11	6	6	36	35.29	35.29
6	14	17	-3	3	9	-21.43	21.43
			Totals	22	104	-51.30	159.38