Adaptive Non-parametric Estimation of Mean and Autocovariance in Regression with Dependent Errors

We develop a fully automatic non-parametric approach to simultaneous estimation of mean and autocovariance functions in regression with dependent errors. Our empirical Bayesian approach is adaptive, numerically efficient and allows for the construction of confidence sets for the regression function. Consistency of the estimators is shown and small sample performance is demonstrated in simulations and real data analysis. The method is implemented in the R package eBsc that accompanies the paper.