Question

In: Statistics and Probability

The following time series shows the sales of a particular product over the past 12 months....

The following time series shows the sales of a particular product over the past 12 months. can be found in the below excel file.

https://drive.google.com/file/d/1gIpr0IBYUGgCIRSO7g3mqZ84F89vJU_P/view?usp=sharing

1. Using the three-month moving average, what is the Mean Squared Error (MSE)?

(Round your answer to 2 decimal places. Negative values should be indicated by a minus sign.)

2.  Using the three-month moving average, what is the forecast for month 13 ?

(Round your answer to 2 decimal places. Negative values should be indicated by a minus sign.)

3. Using the exponential smoothing approach for ? .3 or .7, what is the Mean Squared Error (MSE)?  

(Round your answer to 2 decimal places. Negative values should be indicated by a minus sign.)

4. Using the exponential smoothing approach for , .3 or .7, what is the forecast for month 13?

(Round your answer to 2 decimal places. Negative values should be indicated by a minus sign.)

5. Using the exponential smoothing approach for , .5 or .5, what is the Mean Squared Error (MSE)?

(Round your answer to 2 decimal places. Negative values should be indicated by a minus sign.)

6. Using the exponential smoothing approach for , .5 or .5, what is the forecast for month 13?

(Round your answer to 2 decimal places. Negative values should be indicated by a minus sign.)

7. Does a smoother constant of .3 or .5 provide more accurate forecasts based on MSE ?

.3
.5

Solutions

Expert Solution

Given Following data:

Week Shipments on Time

1 105

2 135

3 120

4 105

5 90

6 120

7 145

8 140

9 100

10 80

11 100

12 110

1.) Please find the solution in below table:

Week Shipments on Time   3 Month Moving Average Error Squared(Error)
1 105
2 135
3 120
4 105 120.00 -15.00 225.00
5 90 120.00 -30.00 900.00 Mean Squared Error
6 120 105.00 15.00 225.00 811.41975308642
7 145 105.00 40.00 1,600.00
8 140 118.33 21.67 469.44 Root Mean Squared Error(RMSE)
9 100 135.00 -35.00 1,225.00 28.4854305406539
10 80 128.33 -48.33 2,336.11
11 100 106.67 -6.67 44.44
12 110 93.33 16.67 277.78

2.) Please find forecast for month 13 in below table:

Week Shipments on Time 3 Month MA
1 105
2 135
3 120
4 105 120.00
5 90 120.00
6 120 105.00
7 145 105.00
8 140 118.33
9 100 135.00
10 80 128.33
11 100 106.67
12 110 93.33
13 96.67

3.) Please find Exponenetial smoothening with alpha = 0.3 in below table:

Week Shipments on Time Exponenetial smoothening    Error Squared Error ?
1 105 105.00 0.00 0.00 0.30
2 135 114.00 21.00 441.00
3 120 115.80 4.20 17.64
4 105 112.56 -7.56 57.15
5 90 105.79 -15.79 249.39 Mean Squared Error(MSE)
6 120 110.05 9.95 98.91 229.20
7 145 120.54 24.46 598.39
8 140 126.38 13.62 185.60 Root Mean Squared Error(RMSE)
9 100 118.46 -18.46 340.91 15.14
10 80 106.92 -26.92 724.93
11 100 104.85 -4.85 23.50
12 110 106.39 3.61 13.01

4.) Using alpha = 0.3, forecast for 13 month is given below:

Week Shipments on Time Exponenetial smoothening
1 105 105.00
2 135 114.00
3 120 115.80
4 105 112.56
5 90 105.79
6 120 110.05
7 145 120.54
8 140 126.38
9 100 118.46
10 80 106.92
11 100 104.85
12 110 106.39
13

107.48

5.) With alpha = 0.5, Please find exponential smoothening below:

Week Shipments on Time Exponenetial smoothening Error Squared Error ?
1 105 105.00 0.00 0.00 0.50
2 135 120.00 15.00 225.00
3 120 120.00 0.00 0.00
4 105 112.50 -7.50 56.25
5 90 101.25 -11.25 126.56 Mean Squared Error
6 120 110.63 9.38 87.89 123.88
7 145 127.81 17.19 295.41
8 140 133.91 6.09 37.13 Root Mean Squared Error
9 100 116.95 -16.95 287.41 11.13
10 80 98.48 -18.48 341.38
11 100 99.24 0.76 0.58
12 110 104.62 5.38 28.95

5.) Forecast for month 13 is given below:

Week Shipments on Time Exponenetial smoothening
1 105 105.00
2 135 120.00
3 120 120.00
4 105 112.50
5 90 101.25
6 120 110.63
7 145 127.81
8 140 133.91
9 100 116.95
10 80 98.48
11 100 99.24
12 110 104.62
13 107.31

6.) With alpha = 0.3, RMSE is: 15.14

With alpha = 0.5, RMSE is: 11.13

Since RMSE is less for alpha = 0.5, so alpha = 0.5 gives better results.

Hence alpha = 0.5 gives accurate results.


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