Problem 15-05 (Algorithmic)

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	15	16	13	17	16

1. Choose the correct time series plot.

   (i)	Time Series Value Week(t)	(ii)	Time Series Value Week(t)
   (iii)	Time Series Value Week(t)	(iv)	Time Series Value Week(t)

   Plot (ii) What type of pattern exists in the data? Horizontal Pattern
2. 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	18
   2	15
   3	16
   4	13	fill in the blank 3
   5	17	fill in the blank 4
   6	16	fill in the blank 5

   MSE: fill in the blank 6 The forecast for week 7: fill in the blank 7
3. 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	18
   2	15	fill in the blank 8
   3	16	fill in the blank 9
   4	13	fill in the blank 10
   5	17	fill in the blank 11
   6	16	fill in the blank 12

   MSE: fill in the blank 13 The forecast for week 7: fill in the blank 14
4. 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? Three-week moving average Explain. The input in the box below will not be graded, but may be reviewed and considered by your instructor.
5. Use trial and error to find a value of the exponential smoothing coefficient that results in a smaller MSE than what you calculated for = 0.2. Find a value of for the smallest MSE. Round your answer to three decimal places. = fill in the blank 17