Consider the following time series data:

Month 1 2 3 4 5 6 7
Value 22 14 20 13 18 22 15

(b) Develop a three-month moving average for this time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation.
MSE:
The forecast for month 8:

(c) Use α = 0.2 to compute the exponential smoothing values for the time series. Compute MSE and a forecast for month 8. If required, round your answers to two decimal places. Do not round intermediate calculation.
MSE:
The forecast for month 8:

(d) Compare the three-month moving average forecast with the exponential smoothing forecast using α = 0.2. Which appears to provide the better forecast based on MSE?

(e) Use trial and error to find a value of the exponential smoothing coefficient α that results in the smallest MSE. Do not round intermediate calculations. Use a two-decimal digit precision for the exponential smoothing coefficient.
α =