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You are a consultant who has been asked to provide a forecast of the US index of

ID: 355978 • Letter: Y

Question

You are a consultant who has been asked to provide a forecast of the US index of industrial production. Using the monthly data given below:

Compute forecasts for periods 5 through 15 using 4-month moving averages.

Compute forecasts for periods 5 through 15 using 4-month weighted moving averages with weights 0.4 (newest period), 0.3, 0.2, and 0.1 (oldest period).

How do these two sets of forecasts compare in terms of accuracy? Compute (i) the Mean Error (bias), (ii) Mean Absolute Deviation (MAD) and (iii) the Mean Absolute Percent Deviation (MAPD). What are these measures telling you?

Period

US Index of Industrial Production

1

108

2

108

3

110

4

106

5

108

6

108

7

105

8

100

9

97

10

95

11

95

12

92

13

95

14

95

15

98

Question-2

For the same data in Question-1, assume that you use exponential smoothing.

Compute forecasts for periods 2 through 15 using exponential smoothing with a = 0.2. Assume a forecast of 100 units for period 1.

Compute forecasts for periods 2 through 15 using exponential smoothing with a = 0.8. Assume a forecast of 100 units for period 1.

How do these two sets of forecasts compare in terms of accuracy? Compute (i) the Mean Error (bias), (ii) Mean Absolute Deviation (MAD) and (iii) the Mean Absolute Percent Deviation (MAPD). What are these measures are telling you?

Period

US Index of Industrial Production

1

108

2

108

3

110

4

106

5

108

6

108

7

105

8

100

9

97

10

95

11

95

12

92

13

95

14

95

15

98

Explanation / Answer

PLEASE FIND BELOW ANSWER TO QUESTION 1 :

Please find below filled up table for ready reference of relevant data

Following may be noted :

Forecast basis 4 month moving average :

Ft = ( At-1 + At-2 + At-3 + At-4 ) / 4

Forecast basis 4 month weighted moving average :

Ft = 0.4 x At-1 + 0.3xAt-2 + 0.2 x At-1 + 0.1xAt-1

Other details as follows :

Error = forecast of US index of industrial production – Actual data of US index of industrial production

Absolute deviation = Absolute difference between actual data on US index of industrial production and corresponding forecast

Absolute Percentage error =   Absolute deviation / Actual data on US industrial production x 100 Thus :

Period

US Index of Industrial production

Forecast ( 4 month moving average)

Error

Absolute deviation

Absolute percent Deviation

Forecast ( 4 month weighted moving average)

Error

Absolute deviation

Absolute percent deviation

1

108

2

108

3

110

4

106

5

108

108

0

0

0.00

107.8

-0.2

0.2

0.19

6

108

108

0

0

0.00

107.8

-0.2

0.2

0.19

7

105

108

3

3

2.86

107.8

2.8

2.8

2.67

8

100

106.75

6.75

6.75

6.75

106.6

6.6

6.6

6.60

9

97

105.25

8.25

8.25

8.51

103.9

6.9

6.9

7.11

10

95

102.5

7.5

7.5

7.89

100.6

5.6

5.6

5.89

11

95

99.25

4.25

4.25

4.47

97.6

2.6

2.6

2.74

12

92

96.75

4.75

4.75

5.16

95.9

3.9

3.9

4.24

13

95

94.75

-0.25

0.25

0.26

94

-1

1

1.05

14

95

94.25

-0.75

0.75

0.79

94.1

-0.9

0.9

0.95

15

98

94.25

-3.75

3.75

3.83

94.4

-3.6

3.6

3.67

SUM =

29.75

39.25

40.52

22.5

34.3

35.29

For forecast basis 4 month moving average :

Mean error = 29.75 /11 = 2.704

Mean Absolute Deviation ( MAD ) = 39.25/11 = 3.568

Mean absolute Percent Error ( MAPE ) = 40.52/11 = 3.683

Note : 11 is number of observations

For forecast basis 4 moth weighted moving average forecast :

Mean error = 22.5/ 11 = 2.045

Mean Absolute Deviation ( MAD ) = 34.3/11 = 3.118

Mean absolute Percent Error ( MAPE ) = 35.29/11 = 3.208

Note : 11 is number of observations

All the values ( i.e. Mean error / MAD/ MAPE ) for forecast basis 4 month weighted moving average is less than forecast basis 4 month moving average.

Therefore , forecast basis 4 month weighted moving average is more accurate.

Period

US Index of Industrial production

Forecast ( 4 month moving average)

Error

Absolute deviation

Absolute percent Deviation

Forecast ( 4 month weighted moving average)

Error

Absolute deviation

Absolute percent deviation

1

108

2

108

3

110

4

106

5

108

108

0

0

0.00

107.8

-0.2

0.2

0.19

6

108

108

0

0

0.00

107.8

-0.2

0.2

0.19

7

105

108

3

3

2.86

107.8

2.8

2.8

2.67

8

100

106.75

6.75

6.75

6.75

106.6

6.6

6.6

6.60

9

97

105.25

8.25

8.25

8.51

103.9

6.9

6.9

7.11

10

95

102.5

7.5

7.5

7.89

100.6

5.6

5.6

5.89

11

95

99.25

4.25

4.25

4.47

97.6

2.6

2.6

2.74

12

92

96.75

4.75

4.75

5.16

95.9

3.9

3.9

4.24

13

95

94.75

-0.25

0.25

0.26

94

-1

1

1.05

14

95

94.25

-0.75

0.75

0.79

94.1

-0.9

0.9

0.95

15

98

94.25

-3.75

3.75

3.83

94.4

-3.6

3.6

3.67

SUM =

29.75

39.25

40.52

22.5

34.3

35.29