Using the data for Problem 16.15 on page 645 that represent the number of new, single-family houses sold in the U.S. from 1992 through 2016 (stored in HouseSales),

a. Fit a third-order autoregressive model to the new single-family homes sold and test for the significance of the third-order autoregressive parameter. (Use α = 0.05.)

b. If necessary, fit a second-order autoregressive model to the new single-family homes sold and test for the significance of the second-order autoregressive parameter. (Use α = 0.05.)

c. If necessary, fit a first-order autoregressive model to the new single-family homes sold and test for the significance of the first-order autoregressive parameter. (Use α = 0.05.)

d. If appropriate, forecast the new single-family homes sold in 2017.