We study a problem of estimating a regression function in a general nonparametric function class. The errors are assumed to be dependent with a known covariance matrix. The minimax risk of the function class under the squared L_2 loss is considered. Minimax rates of convergence are determined in terms of the massiveness (characterized by metric entropy) of the class and behavior of the covariance matrix of the errors. It is shown that under mild conditions, the minimax risk is at the worse rate between two quantities: the minimax risk of the same class but under the assumption of i.i.d.\ errors, and the minimax risk of estimating the mean of the regression function. The finding of separate roles of the function class and dependence of errors is somewhat surprising. Examples of several function classes under different covariance structures including both short and long range dependences are given.
 
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