Question on auto-correlated residuals and time-series

On page 415, problem 16, the model that they employed for the sales of Home Depot includes the last month’s lag as well as 4 quarter ago’s lags. The auto-correlation was between today’s residuals and 4 month’s agos residuals is 0.8496, and since there are 40 observations, the T-error is 5.37. Because this establishes that there is an auto-correlation between today’s error and 4 Q’s ago’s error, we introduce this lagging factor into the equation. So, the equation to predict the change in profit margin for home depot as a function of last month’s data and 4Q’s ago’s data. However, in problem 17 on page 416-417, they have a table of auto-correlation, and none of these T-values are significant. In spite of this, they still employ the Lag 4 variable, even though it doesn’t have the highest T-value. Doesn’t their methodologies contradict one another? On one hand, they accept a high T-valued auto-correlation, but in the next problem, they (somewhat arbitrarily) accepted a low-T-value auto-correlation.

that does look weird.

please help me.

I’m not sure about the reasoning. I think you should continue on and do some questions and see if it shows and get a good feel for the general material.