Prediction of future time-series values, based on a finite set of available observations, is a prevalent problem in many branches of science and engineering. By making the assumption that the time series is either Gaussian or linear, the classical technique of linear prediction may be fruitfully applied. Unfortunately, few, if any, real-world time series are linear or Gaussian, and as such, prediction methods that can accommodate a larger class of time series are needed. In this spirit, nonparametric predictors based on the Nadaraya-Watson kernel regression estimator are examined. Using mixing conditions to quantify the dependence structure of time series, it is shown that the kernel predictor performs as well, asymptotically (in the mean square sense), as the conditional mean (optimal) predictor. In addition, a computationally efficient predictor based on the recursive kernel regression estimator is introduced. Its performance is comparable to that of the kernel predictor.