Refer to the data file Hourly Earnings, showing earnings over 24 months. Denote the observations xt (t = 1, 2, .., 24). Now, form the series of first differences:
zt = xt – xt-1 (t = 2, 3, c, 24)
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.