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
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