I need a step-by-step explanation on how to solve this problem. Method of Time S
ID: 397457 • Letter: I
Question
I need a step-by-step explanation on how to solve this problem.
Method of Time Series
Use F7 period:
Please solve for the following:
a. Naïve Average
b. Arithmetic Average
c. Moving Average (n=3)
d. Weight Moving Average (n=2), weight = 8, 2
e. Based on MSE
Week Of Pints Used Forecast |A1 – F1|
August 31 360
September 7 389
September 14 410
September 21 381
September 28 368
October 5 374
Explanation / Answer
a)
Naïve Method: The forecast of the period is equal to actual value of previous period.
Naïve Method
Absolute Error
Squared Error
Period
Pints used
Forecast
|A - F|
(A-F)2
1
360
-
2
389
360
|389-360|
= 29
(389-360)2
= 841
3
410
389
21
441
4
381
410
29
841
5
368
381
13
169
6
374
368
6
36
374
Total
98
2328
Average
19.6
465.6
Mean Absolute Error (MAE)
Mean Squared Error (MSE)
b.) Arithmetic Average Method: The forecast of period is equal to average of all the actual values of previous periods.
Arithmetic Average
Absolute Error
Squared Error
Period
Pints used
Forecast
|A - F|
(A-F)2
1
360
-
2
389
360
29
841
3
410
(389+360)/2
=374.5
35.5
1260.25
4
381
(410+389+360)/3
= 386.3333
5.333333
28.44444
5
368
(381+410+389+360)/3
= 385
17
289
6
374
381.6
7.6
57.76
7
380.33
Total
94.43333
2476.454
Average
18.88667
495.2909
MAE
MSE
c)
Moving Average (n = 3): The forecast of the period is equal to the average of actual values of three recent previous periods.
Forecast of the period 5 = (381+410+389)/3 = 393.33
Moving Average (n = 3)
Absolute Error
Squared Error
Period
Pints used
Forecast
|A - F|
(A-F)2
1
360
-
2
389
-
3
410
-
4
381
386.3333
5.333333
28.44444
5
368
393.3333
25.33333
641.7778
6
374
386.3333
12.33333
152.1111
7
374.33
Total
43
822.3333
Average
14.33333
274.1111
MAE
MSE
d)
Weighted Moving Average: (n = 2), (weights = 8, 2)
The 2-month weighted moving average is calculated as follows:
Ft = (w t-1At-1 + w t-2At-2 /( w t-1 + w t-2 + w t-3)
w t-1 = weight for the most recent period (t-1)= 8
w t-2 = weight for the most recent period (t-2) = 2
F5 = (8*A4 + 2*A3) /( 8 + 2) = (8*381 + 2*410) /( 8 + 2) = 386.8
Weighted Moving Average (n = 2), Weight = 0.8,0.2
Period
Pints used
Forecast
|A - F|
(A-F)2
1
360
-
2
389
-
3
410
383.2
26.8
718.24
4
381
405.8
24.8
615.04
5
368
386.8
18.8
353.44
6
374
370.6
3.4
11.56
7
372.8
Total
73.8
1698.28
Average
18.45
424.57
MAE
MSE
e)
Mean Absolute Error = average of absolute forecast error for the forecasted periods.
Mean Squared Error = average of squared forecast error for the forecasted periods.
Forecast error = Actual – Forecast
Method
MSE
Naïve Method
465.6
Arithmetic Average
495.2909
Moving Average (n = 3)
274.1111
Weighted Moving Average
424.57
According to MSE, the method which provides minimum MSE value is more accurate forecast method. Thus, Moving Average (n=3) method is more accurate method.
Naïve Method
Absolute Error
Squared Error
Period
Pints used
Forecast
|A - F|
(A-F)2
1
360
-
2
389
360
|389-360|
= 29
(389-360)2
= 841
3
410
389
21
441
4
381
410
29
841
5
368
381
13
169
6
374
368
6
36
374
Total
98
2328
Average
19.6
465.6
Mean Absolute Error (MAE)
Mean Squared Error (MSE)
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