Question

Problem 15-05 (Algorithmic)

Consider the following time series data.

Week	1	2	3	4	5	6
Value	16	13	18	11	15	14

1. 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	16
   2	13
   3	18
   4	11
   5	15
   6	14

   
   MSE:
   
   The forecast for week 7:
   
2. 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	16
   2	13
   3	18
   4	11
   5	15
   6	14

   
   MSE:
   
   The forecast for week 7:
3. Use trial and error to find a value of the exponential smoothing coefficient alpha that results in a smaller MSE than what you calculated for alpha = 0.2. Find a value of alpha for the smallest MSE. Round your answer to three decimal places.
   
   Alpha = ________

Please solve for part C! Thank you !

Answer 1

c). Alpha for which MSE is minimized = 0.142

	alpha	0.142
Formula		F2 = A1; Fn = Fn-1 + (a*En-1)	E = A-F	(A-F)^2
Week (n)	Time Series Value (A)	Forecast (F)	Forecast Error ('E)	Sqaured Forecast Error
1	16
2	13	16.00	(3.00)	9.00
3	18	15.57	2.43	5.88
4	11	15.92	(4.92)	24.19
5	15	15.22	(0.22)	0.05
6	14	15.19	(1.19)	1.42
7		15.02
			MSE	8.108