Summary: New approaches for chaotic time series prediction are introduced. We first summarize and evaluate the existing local prediction models, then propose optimization models and new algorithms to modify procedures of local approximations. A modification to the choice of sample sets is given, and the zeroth-order approximation is improved by a linear programming method. Four procedures of first-order approximation are compared, and corresponding modified methods are given. Lastly, the idea of nonlinear feedback to raise predicting accuracy is put forward. In the end, we discuss two important examples, i.e., the Lorenz system and Rössler system, and the simulation experiments indicate that the modified algorithms are effective.