Problem 15-05 (Algorithmic)

Consider the following time series data.

Week	1	2	3	4	5	6
Value	18	13	16	11	17	14

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)

   CHOOSE ONE: Plot (i)Plot (ii)Plot (iii)Plot (iv)

   What type of pattern exists in the data?

   CHOOSE ONE: Horizontal PatternTrend 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	13
   3	16
   4	11	_________
   5	17	_________
   6	14	_________

   MSE: _________ The forecast for week 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	13	_________
   3	16	_________
   4	11	_________
   5	17	_________
   6	14	_________

   MSE: _________ The forecast for week 7: _________
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?

   CHOOSE ONE: Three-week moving average/ Exponential smoothing

   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. = _________