Question  2. Consider the following time series data: 2Month Value 20 15 23 6 4 13 6 18 25 10 8 10 9 24 12 10 21 13 19 14 15 la. Use a α # 0.25 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for Month 12. b. Compare the two-month moving average forecast with the exponential smoothing forecast using a 0.25. Which appears to 17 provide the better forecast based on MSE? rial and error to find a value of the exponential smoothing coofficilent a that results in a smaller MSE than what you 19. calculated for α :0.25
Can you piease Show how got the answer neps me Undlerstand H better hank you So much

a. If Y(t) is the value for month t, the forecast for month t+1 using exponential smoothing model is We will set the first month forecast as the the actual value, that is F(1) = 20. The forecast for month 2 is We compute the 2 month moving average forecast using For example the forecast for month 3 is Since we want to compare a 2 month moving average with exponential forecast, we will calculate the MSE (Mean Square error) using the data from 3rd month to month 11 Prepare the following sheet We have kept the value of alpha in a separate cell so that we can do the trial and error required in part c)

get this a) MSE for exponential forecast with alpha=0.025 is 34.99, Forecast for the month of 12 is 19.09

b) The MSE for 2 month moving average forecast is 48.81 and it is larger than the MSE for exponential smoothing forecast. Hence we can say that exponential smoothing method provides a better forecast based on MSE

c. Now we can use trial and error by changing the value of alpha in cell C1. Try values between 0 and 1 starting from 0.01 to 1.

Or we can use the solver in excel to find the value of alpha which will give the lowest MSE.

Set up the solver using data---> solver get this We can see that for alpha=0.03, results in a smaller MSE than we calculated for alpha=0.25

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