• seemingly unrelated regression;
  • non-parametric model;
  • two-stage estimation;
  • asymptotic normality

This article is concerned with the inference on seemingly unrelated non-parametric regression models with serially correlated errors. Based on an initial estimator of the mean functions, we first construct an efficient estimator of the autoregressive parameters of the errors. Then, by applying an undersmoothing technique, and taking both of the contemporaneous correlation among equations and serial correlation into account, we propose an efficient two-stage local polynomial estimation for the unknown mean functions. It is shown that the resulting estimator has the same bias as those estimators which neglect the contemporaneous and/or serial correlation and smaller asymptotic variance. The asymptotic normality of the resulting estimator is also established. In addition, we develop a wild block bootstrap test for the goodness-of-fit of models. The finite sample performance of our procedures is investigated in a simulation study whose results come out very supportive, and a real data set is analysed to illustrate the usefulness of our procedures.