Question

# Problem 15-05 (Algorithmic) Consider the following time series data. Week 1 2 3 4 5 6...

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 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.

= ______

a).

 Formula (An-1 + An-2 + An-3)/3 A-F (A-F)^2 Week (n) Time Series Value (A) Forecast (F) Error (E) Squared Forecast Error 1 16 2 13 3 18 4 11 15.67 (4.67) 21.78 5 15 14.00 1.00 1.00 6 14 14.67 (0.67) 0.44 7 13.33

Forecast for week 7 = 13.33

MSE = Sum of squared forecast error/number of errors =  (21.78 + 1.00 + 0.44)/3 = 7.74

b). For forecast at n = 2, F2 is assumed to be the same as the actual value for n = 1, A1. For the remaining forecasts, using alpha = 0.2, the forecast Fn is calculated as Fn-1 + alpha*Errorn-1

 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 15.40 2.60 6.76 4 11 15.92 (4.92) 24.21 5 15 14.94 0.06 0.00 6 14 14.95 (0.95) 0.90 7 14.76

Forecast for week 7 = 14.76

MSE = Sum of squared forecast error/number of errors =  (9.00 + 6.76 + 21.21 + 0.00 + 0.90)/5 = 8.17

c). Using the table in part (b) and excel solver, the value of alpha at which MSE is minimized is 0.142 and MSE = 8.108

 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

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