Refer to the data file Hourly Earnings, showing earnings over 24 months. Denote the observations $x_t(t=1,2, \ldots, 24)$. Now, form the series of first differences:
$$
z_t=x_t-x_{t-1}(t=2,3, \ldots, 24)
$$
Fit autoregressive models of orders 1-4 to the series $z_t$. 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 $z_t$, where $t=25,26$, and 27 . Hence, obtain forecasts of earnings for the next 3 months.