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Category > Management Posted 04 May 2018 My Price 5.00

Quiet Mental Breakdown

Weekly income for Quiet Mental Breakdown, an online psychology firm, is provided below. Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average gives a better forecast.

Forecasting Problem Set

 

 

F-1 Weekly income for Quiet Mental Breakdown, an online psychology firm, is provided below.  Determine, on the basis of minimizing the mean square error, whether a three-period or four-period simple moving average gives a better forecast.

 

Week

Income

 

 

 

 

 

 

 

1

980

 

 

 

 

 

 

 

2

1040

 

 

 

 

 

 

 

3

1120

 

 

 

 

 

 

 

4

1050

 

 

 

 

 

 

 

5

960

 

 

 

 

 

 

 

6

990

 

 

 

 

 

 

 

7

1030

 

 

 

 

 

 

 

8

1260

 

 

 

 

 

 

 

9

1240

 

 

 

 

 

 

 

10

1100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

F-2 Using the table above, what is your forecast for week 11 using a three-period weighted average with weights of .6, .3 and .1?  The weights are stated from the most current time period to the oldest time period. 

 

F-3 Using the table above, with smoothing constants of α = .10 and then α = .30, forecast income for week 11 using exponential smoothing.

 


 

Solutions

F-1 On the basis of minimizing the mean square error, the three-period simple moving average gives a better forecast (smaller MSE).  

 

Week

Actual Value

Moving Average

Error

Squared Error

1

980

 

 

 

2

1040

 

 

 

3

1120

 

 

 

4

1050

1046.67

3.33

11.11

5

960

1070.00

-110.00

12100.00

6

990

1043.33

-53.33

2844.44

7

1030

1000.00

30.00

900.00

8

1260

993.33

266.67

71111.11

9

1240

1093.33

146.67

21511.11

10

1100

1176.67

-76.67

5877.78

11

 

1200.00

 

 

MSE=114,355.6/7=16336.51

 

 

 

 

 

Week

Actual Value

Moving Average

Error

Squared Error

1

980

 

 

 

2

1040

 

 

 

3

1120

 

 

 

4

1050

 

 

 

5

960

1047.50

-87.50

7656.25

6

990

1042.50

-52.50

2756.25

7

1030

1030.00

0.00

0.00

8

1260

1007.50

252.50

63756.25

9

1240

1060.00

180.00

32400.00

10

1100

1130.00

-30.00

900.00

11

 

1157.50

 

MSE=107,468.8/6=17911.46

 

F-2

Week

Income

 

1

980

 

2

1040

 

3

1120

 

4

1050

1082.0

5

960

1070.0

6

990

1003.0

7

1030

987.0

8

1260

1011.0

9

1240

1164.0

10

1100

1225.0

11

 

1158.0

12

 

 

Example week 4:     980(.1)+1040(.3)+1120(.6)=1082

Example week 11: 1260(.1)+1240(.3)+1100(.6)=1158


F-3 Using the table, with smoothing constants of α = .10 and then α = .30, forecast income for week 11 using exponential smoothing.

 

Week

Income

α = .10

 

1

980

 

 

2

1040

980.00

 

3

1120

986.00

1040(.1)+ 980(.9)= 986

4

1050

999.40

1120(.1)+ 986(.9)= 999.40

5

960

1004.46

1050(.1)+ 999.40(.9)=1004.46

6

990

1000.01

 960(.1)+1004.46(.9)=1000.01

7

1030

999.01

 990(.1)+1000.01(.9)= 999.01

8

1260

1002.11

1030(.1)+ 999.01(.9)=1002.11

9

1240

1027.90

1260(.1)+1002.11(.9)=1027.90

10

1100

1049.11

1240(.1)+1027.90(.9)=1049.10

11

 

1054.20

1100(.1)+1049.10(.9)=1054.20

 

Week

Income

α = .30

1

980

 

2

1040

980.00

3

1120

998.00

4

1050

1034.60

5

960

1039.22

6

990

1015.45

7

1030

1007.82

8

1260

1014.47

9

1240

1088.13

10

1100

1133.69

11

 

1123.58

 

 

 


 

 

Answers

(5)
Status NEW Posted 04 May 2018 08:05 PM My Price 5.00

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