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

Question

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

Explanation / Answer

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:

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

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

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

107.48

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

5.) Forecast for month 13 is given below:

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.

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

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