Altman (1990) and Hart (1991) have shown that kernel regression can be an effective method for estimating an unknown mean function when the errors are correlated. However, the optimal bandwidth for kernel smoothing depends strongly on the correlation function, as do confidence bands for the regression curve.

In this paper, the simultaneous estimation of the regression and correlation functions is explored. An iterative technique analogous to the iterated Cochrane-Orcutt method for linear regression (Cochrane and Orcutt, 1949) is shown to perform well. However, for moderate sample sizes, stopping after the first iteration produces better results.

An interesting feature of the simultaneous method is that it performs best when different kernels are used to estimate the regression and correlation functions. For the regression function, unimodal kernels are known to be optimal. However, examination of the mean squared error of the correlation estimator suggests that a bimodal kernel will perform better for estimating correlations. Use of a bimodal kernel or estimating the correlation function, followed by use of a unimodal kernel for estimating the regression function at the final step, performed best in a simulation study.