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Keywords:

  • autoregressive error process;
  • heteroscedastic;
  • semiparametric estimators;
  • difference-based estimation approach

We consider a heteroscedastic nonparametric regression model with an autoregressive error process of finite known order p. The heteroscedasticity is incorporated using a scaling function defined at uniformly spaced design points on an interval [0,1]. We provide an innovative nonparametric estimator of the variance function and establish its consistency and asymptotic normality. We also propose a semiparametric estimator for the vector of autoregressive error process coefficients that is inline image consistent and asymptotically normal for a sample size T. Explicit asymptotic variance covariance matrix is obtained as well. Finally, the finite sample performance of the proposed method is tested in simulations.