Contributions to the disaster relief fund for a national charity average around $1 million a month and do not exhibit trend or seasonal effects. Data on the most recent 12 months is given in the following table.

Month ______________ Contributions

1 ................................. 1,074,844

2 .................................... 780,433

3 ................................. 1,082,218

4 ................................. 1,009,653

5 ................................. 1,066,739

6 ................................. 1,297,010

7 .................................... 978,685

8 ................................. 1,108,218

9 ................................. 1,019,778

10 ................................... 999,380

11 ................................ 1,041,070

12 ................................... 821,189

a. Compute a forecast for next month's contributions by using a 4-month moving average. What is the forecast? What is the MSE for the last five observations?

b. Can you reduce the MSE for the last five observations by changing the moving-average window? (Try 5- to 7-week windows.)

c. Compute a forecast for next month's contributions by using exponential smoothing with α = 0.25. What is the forecast? What is the MSE for the last five observations?

d. Can you reduce the MSE for the last five observations by changing the smoothing constant α?