Question

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13...

Consider the following time series data.

Week 1 2 3 4 5 6

Value 18 13 15 13 15 15

 (b) Develop a three-week moving average for this time series. Compute MSE and a forecast for week 7. If required, round your answers to two decimal places.
 (c) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for week 7. If required, round your answers to two decimal places.

(d) Use trial and error to find a value of the exponential smoothing coefficient α that results in a smaller MSE than what you calculated for α = 0.20. Use a two-decimal digit precision.

b)

 3 week Time period Actual Value(A) Moving avg. Forecast(F) Forecast error E=|A-F| Squared Forecast Error 1 18 2 13 3 15 4 13 15.33 2.33 5.44 5 15 13.67 1.33 1.78 6 15 14.33 0.67 0.44 Total 4.33 7.67 Average 1.44 2.56 MAD MSE

MSE =2.56

forecast =14.33
c)

 Time period Actual Value(A) Forecast(F) Forecast error E=A-F Squared Forecast Error 1 18 2 13 18.00 5.00 25.00 3 15 17.00 2.00 4.00 4 13 16.60 3.60 12.96 5 15 15.88 0.88 0.77 6 15 15.70 0.70 0.50 Total 12.18 43.23 Average 2.44 8.65 MAD MSE

MSE =8.65

forecast =15.56

d)value of alpha =0.62

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