In: Statistics and Probability
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 |
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.