16.31 Refer to the data file Hourly Earnings, showing earnings over 24 months. Denote the observations xt 1t = 1, 2,

c, 242. Now, form the series of first differences:

zt = xt - xt-1 1t = 2, 3,

c, 242 Fit autoregressive models of orders 1–4 to the series zt.

Using the approach of this section for testing the hypothesis that the autoregressive order is p - 1 against the alternative of order p, with a 10% significance level, select one of these models. Using the selected model, find forecasts for zt, where t = 25, 26, and 27. Hence, obtain forecasts of earnings for the next 3 months.