Question
In: Operations Management
Question 1. Consider the following time series data. Week 1 2 3 4 5 6 Value...
Question 1. Consider the following time series data.
|
Week |
1 |
2 |
3 |
4 |
5 |
6 |
|
Value |
118 |
113 |
116 |
111 |
117 |
114 |
-
Construct a time series plot. What type of pattern exists in the data?
-
Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7.
-
Use a =0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7.
Compare the three-week moving average forecast with the exponential smoothing forecast using =0.2. Which appears to provide the better forecast based on MSE? explain.
Solutions
Expert Solution
The time series plot=
The time series plot shown above has a horizontal pattern.
Answer-
| Week | Value | The 3-week moving average forecast | The 3-week moving average forecast | Error | Error^2 |
| 1 | 118 | ||||
| 2 | 113 | ||||
| 3 | 116 | ||||
| 4 | 111 | (118+113+116)/3 | 115.67 | -4.67 | 21.78 |
| 5 | 117 | (113+116+111)/3 | 113.33 | 3.67 | 13.44 |
| 6 | 114 | (116+111+117)/3 | 114.67 | -0.67 | 0.44 |
| 7 | (111+117+114)/3 | 114 | Sum | 35.67 |
MSE=35.67/3=11.89
Forecast for week 7=114
Answer=
| Week | Value | Exponential smoothening forecast | Exponential smoothening forecast | Error | Error^2 |
| 1 | 118 | 118.00 | 0.00 | 0.00 | |
| 2 | 113 | 118+0.2*(118-118) | 118.00 | -5.00 | 25.00 |
| 3 | 116 | 118+0.2*(113-118) | 117.00 | -1.00 | 1.00 |
| 4 | 111 | 117+0.2*(116-117) | 116.80 | -5.80 | 33.64 |
| 5 | 117 | 116.8+0.2*(111-116.8) | 115.64 | 1.36 | 1.85 |
| 6 | 114 | 115.64+0.2*(117-115.64) | 115.91 | -1.91 | 3.66 |
| 7 | 115.91+0.2*(114-115.91) | 115.53 | Sum | 65.15 |
MSE=65.15/6=10.86
Forecast for week 7=115.53
Answer= Exponential smoothening with alpha 0.2 has the better forecast as it has less value of MSE
keosha answered 1 year agoRelated Solutions
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