Stability of the partial sum process of residuals in a multiple linear regression model

We discuss a refinement of the MacNeill's result (1978) on limit behavior of the so-called residual process of a linear regression model. We study stability of the process with respect to $L_2$-variations of the regressor. As an example, we consider the case when the regressor is a smooth function of the variational series based on $n$ identically distributed observations not necessarily independent.