Nonparametric regression with rescaled time series errors


Correspondence to: Michael Levine, Department of Statistics, 250 N. University St., Department of Statistics, Purdue University, West Lafayette, IN 47907-2066.



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 math formula 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.