Artificial Neural networks (ANN) are powerful and effective tools in time-series applications. The first aim of this paper is to diagnose better and more efficient ANN models (Back Propagation, Radial Basis Function Neural networks (RBF), and Recurrent neural networks) in solving the linear and nonlinear time-series behavior. The second aim is dealing with finding accurate estimators as the convergence sometimes is stack in the local minima. It is one of the problems that can bias the test of the robustness of the ANN in time series forecasting. To determine the best or the optimal ANN models, forecast Skill (SS) employed to measure the efficiency of the performance of ANN models. The mean square error and the absolute mean square error were also used to measure the accuracy of the estimation for methods used. The important result obtained in this paper is that the optimal neural network was the Backpropagation (BP) and Recurrent neural networks (RNN) to solve time series, whether linear, semilinear, or non-linear. Besides, the result proved that the inefficiency and inaccuracy (failure) of RBF in solving nonlinear time series. However, RBF shows good efficiency in the case of linear or semi-linear time series only. It overcomes the problem of local minimum. The results showed improvements in the modern methods for time series forecasting.