Abstract We consider the regression model yt = η t + e t , t = 0, 1, …, n − 1, where y t are scalar observations, η t is the unknown regression function, and e t are unobservable errors generated by a zero-mean weakly stationary process, independent of η t and with completely unknown autocorrelation structure. We propose a data-driven method for selecting a parametric or nonparametric estimator of η t . The method is based on cross-validation in the frequency domain and requires no assumptions about the form of the estimator or the error correlations. It does, however, require the discrete Fourier transform (DFT) of the signal η t to be a smooth complex function of frequency, as is the case, for example, with transient signals or growth and decay curves. After giving some general motivations for the method, we focus on the special case of linear estimators of a nonparametric regression function, including both kernel and spline estimators. For these estimators, we develop efficient methods of evaluating t...