Regression model fitting with long memory errors

This paper studies a class of tests useful for testing the goodness-of-fit of a regression model when the errors have long memory. These tests are based on a class of empirical processes marked by certain residuals. The paper gives their large sample behavior under null hypotheses. The design variables are assumed to be either known constants or random, independent of the errors. The errors are assumed to be either a non-linear function of a long memory Gaussian process or a moving average type. Under some conditions on the fitted parametric regression function and in the case of random designs, these tests are asymptotically distribution free and easier to implement than under the classical setting of independent and identically distributed errors. A similar statement does not hold for the non-random designs. (C) 1998 Elsevier Science B.V. All rights reserved.