Models that may appear to have different properties may in fact produce res
iduals that differ only in subtle ways. By analysing the relationships betw
een model residuals the problems in distinguishing between models can perha
ps be discovered: as illustrated by the econometric examples considered. Re
gressing residuals gives the long-memory residual, which is the difference
between two models, but this difference is very subtle and deeply hidden, w
hich explains why the traditional standard technique does not find this dif
ference.