Adaptive semiparametric estimation in the presence of autocorrelation of unknown form

In a time series regression model the residual autoregression function is an unknown, possibly non-linear, function. It is estimated by non-parametric kernel regression. The resulting least-squares estimate of the regression function is shown to be adapative, in the sense of having the same asymptotic distribution, to first order, as estimates based on knowledge of the autoregression function. Also, a Monte Carlo experiment about the behaviour of the estimator is described.