Spline estimation of partially linear regression models for time series with correlated errors

Partially linear regression smoothing is a useful technique for modeling time series. Using polynomial splines and a weighted least squares method, this study investigates a class of partially linear regression models of time series with correlated errors. $\sqrt{n}$-consistency of parametric estimators and the convergence rate of the nonparametric estimator are derived under some suitable conditions. Simulations reveal that the proposed approach is more valid than that of ignoring correlated errors. Moreover, the importance of considering autoregressive errors is illustrated by making multi-step-ahead forecasts for Australian blow-fly data.