Consider the following time series data.
Week | 1 | 2 | 3 | 4 | 5 | 6 |
Value | 19 | 14 | 17 | 12 | 17 | 14 |
Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.
Week | Time Series Value |
Forecast |
---|---|---|
1 | 19 | |
2 | 14 | |
3 | 17 | |
4 | 12 | |
5 | 17 | |
6 | 14 |
MSE:
The forecast for week 7:
Use = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. Round your answers to two decimal places.
Week | Time Series Value |
Forecast |
---|---|---|
1 | 19 | |
2 | 14 | |
3 | 17 | |
4 | 12 | |
5 | 17 | |
6 | 14 |
MSE:
The 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.
ANSWER
Please refer below table which presents forecast and MSE basis 3 week moving average :
Week |
Value |
Forecast |
Squared error |
1 |
19 |
||
2 |
14 |
||
3 |
17 |
||
4 |
12 |
16.67 |
21.78 |
5 |
17 |
14.33 |
7.11 |
6 |
14 |
15.33 |
1.78 |
7 |
14.33 |
||
SUM = |
30.67 |
It may be noted that :
a) Forecast for period t = ( Value for period t-1 + Value for period t-2 + Value for period t-2) /3
Accordingly forecast for week 7 = 14.33
b) Squared error for period t = ( Forecast for period t – Value for period t ) ^2
Sum of squared error = 30.67
Mean square error ( MSE ) = Sum of squared error / Number of data ( i.e. 3 ) = 30.67/3 = 10.22
Please refer below table for forecast and MSE basis exponential smoothing method
Week |
Value |
Forecast |
Squared error |
1 |
19 |
19.00 |
0.00 |
2 |
14 |
19.00 |
25.00 |
3 |
17 |
18.00 |
1.00 |
4 |
12 |
17.80 |
33.64 |
5 |
17 |
16.64 |
0.13 |
6 |
14 |
16.71 |
7.35 |
7 |
16.17 |
||
SUM = |
67.12 |
It may be noted :
Where, Ft , Ft-1 = Forecasts for period t and t-1 respectively
Vt-1 = Value for period t-1
Alpha = exponential smoothing constant = 0.2
We are also making assumption that forecast for week 1 = 19
Accordingly forecast for week 7 = 16.17
Sum of squared error = 67.12
Mean square error ( MSE ) = sum of square error / Number of data ( 6 ) = 67.12/6 = 11.186
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