Repeat given Exercise, but for a second-order autoregressive forecasting equation. Compare the MAD values for forecasts generated by the two equations and indicate which one is the better fit to these data.
Exercise
The Consumer Price Index from 1961 through 2004 is in file XR18085, with 1982-1984 = 100 and 1961 coded as t = 1. Construct a first-order autoregressive forecasting equation for these data, calculate the mean absolute deviation (MAD) for the fit of the forecast values to the actual values, then use the equation to forecast the CPI for 2005.