Model evaluation based on residual analysis of two similar models

Models that may appear to have different properties may in fact produce residuals that differ only in subtle ways. By analysing the relationships between model residuals the problems in distinguishing between models can perhaps be discovered, as illustrated by the econometric examples considered. Regressing residuals gives the long-memory residual, which is the difference between two models, but this difference is very subtle and deeply hidden, which explains why the traditional standard technique does not find this difference.