This paper considers estimation of the regression function and its derivatives in nonparametric regression with fractional time series errors. We focus on investigating the properties of a kernel dependent function V (delta) in the asymptotic variance and finding closed form formula of it, where delta is the long-memory parameter. - General solution of V (delta) for polynomial kernels is given together with a few examples. It is also found, e.g. that the Uniform kernel is no longer the minimum variance one by strongly antipersistent errors and that, for a fourth order kernel, V (delta) at some delta > 0 is clearly smaller than R(K). The results are used to develop a general data-driven algorithm. Data examples illustrate the practical relevance of the approach and the performance of the algorithm
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