A Better Way The traditional approach described in Part 2 did not detect the presence of mean-heterogeneity and so it misidentified temporal dependence as the sole source of misspecification associated with the original LRM.
On the basis of figures 1-3 we can summarize our progress in detecting potential departures from the LRM model assumptions to probe thus far:
|(H) Heterogeneity:||Identically Distributed||mean-heterogeneity|
Discriminating and Amplifying the Effects of Mistakes We could correctly assess dependence if our data were ID and not obscured by the influence of the trending mean. Although, we can not literally manipulate relevant factors, we can ‘subtract out’ the trending mean in a generic way to see what it would be like if there were no trending mean. Here are the detrended xt and yt.