Nonparametric regression techniques are often sensitive to the presence of correlation in the errors. The practical consequences of this sensitivity are explained, including the breakdown of several popular data-driven smoothing parameter selection methods. We review the existing literature in kernel regression, smoothing splines and wavelet regression under correlation, both for short-range and long-range dependence. Extensions to random design, higher dimensional models and adaptive estimation are discussed.
"Nonparametric Regressin with Correlated Errors." Statist. Sci. 16 (2) 134 - 153, May 2001. https://doi.org/10.1214/ss/1009213287