Using the data for Problem 16.17 concerning the number of automobiles assembled in the United States from 1999 to 2018 (stored in Auto Production),

a. Fit a third-order autoregressive model to the number of automobiles assembled in the United States and test for the significance of the third-order autoregressive parameter. (Use a = 0.05.)

b. If necessary, fit a second-order autoregressive model to the number of automobiles assembled in the United States and test for the significance of the second-order autoregressive parameter. (Use a = 0.05.)

c. If necessary, fit a first-order autoregressive model to the number of automobiles assembled in the United States and test for the significance of the first-order autoregressive parameter. (Use a = 0.05.)

d. Forecast the number of automobiles assembled in the United States for 2019.

Problem 16.17

The file Auto Production contains the number of automobiles assembled in the United States (in thousands) from 1999 to 2018.
a. Plot the data.
b. Compute a linear trend forecasting equation and plot the trend line.
c. Compute a quadratic trend forecasting equation and plot the results.
d. Compute an exponential trend forecasting equation and plot the results.
e. Which model is the most appropriate?
f. Using the most appropriate model, forecast the U.S. automobiles assembled for 2019.