Consider the following time series data.
Year
Value
1
234
2
287
3
255
4
310
5
298
6
250
7
302
8
267
9
225
10
336
a. Construct a time series plot. What type of pattern exists in the data?b. Develop a three-year moving average for this time series. Compute MSE and a forecast for the year 11.
What will be an ideal response?
a.
The time series data appear to follow a horizontal pattern.
b.
Year | Value | Forecast | Forecast Error | Squared Forecast Error |
1 | 234 | |||
2 | 287 | |||
3 | 255 | |||
4 | 310 | 258.67 | 51.33 | 2,635.11 |
5 | 298 | 284.00 | 14.00 | 196.00 |
6 | 250 | 287.67 | -37.67 | 1,418.78 |
7 | 302 | 286.00 | 16.00 | 256.00 |
8 | 267 | 283.33 | -16.33 | 266.78 |
9 | 225 | 273.00 | -48.00 | 2,304.00 |
10 | 336 | 264.67 | 71.33 | 5,088.44 |
Total | 12,165.11 | |||
MSE = 12,165.11/7 = 1,737.87
The forecast for year 11 is 
= (y8 + y9 + y10) / 3 = (267 + 225 + 336) / 3 = 276.00.
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