  This paper studies nonparametric regression with long memory (LRD) errors and
predictors. First, we formulate general conditions which guarantee the standard
rate of convergence for a nonparametric kernel estimator. Second, we calculate
the Mean Integrated Squared Error (MISE). In particular, we show that LRD of
errors may influence MISE. On the other hand, an estimator for a shape function
is typically not influenced by LRD in errors. Finally, we investigate
properties of a data-driven bandwidth choice. We show that Averaged Squared
Error (ASE) is a good approximation of MISE, however, this is not the case for
a cross-validation criterion.
