ABSTRACT

Abstract. Let (X_i, Y_i), i= 0, pL 1,… denote a bivariate stationary time series with X_i being R^d-valued and Y_i being real-valued. We consider the regression model Y_i=θ(X_i) +Z_i, where θ(·) is an unknown function and Z_i is an autoregressive process. Given a realization of length n, we examine the problem of estimating the nonparametric function θ(·) and the parametric component Z_i. Under appropriate regularity conditions, it is shown that both components can be optimally estimated.