This dissertation aims to develop an effective and practical method to forecast chaotic time series. Chaotic behaviour has been observed in the areas of marketing, stock markets, supply chain management, foreign exchange rates, weather forecasting and many others. An effective forecasting model can reduce the potential risks and uncertainty and facilitate planning and decision making in chaotic systems. In this study, residual analysis using a combination of the embedding theorem and ensemble artificial neural networks is adopted to forecast chaotic time series. Based on the embedding theorem, the embedding parameters are determined and the time series is reconstructed into proper phase space points. The embedded phase space points are fed into the first neural network and trained. The weights and biases are kept to predict the future values of phase space points and accordingly to obtain future values of chaotic time series. The residual of the predicted time series is further analyzed; and, if a chaotic behaviour is observed, then the residuals are processed as a new chaotic time series and predicted. This iterative residual analysis can be repeated several times depending on the desired accuracy level and computational efficiency. Finally, the last neural network is trained using neural networks' result values of the time series and the residuals as input and the original time series as output. The initial weights and biases of the neural networks are improved using genetic algorithms. Taguchi's design of experiments is adopted to identify appropriate factor-level combinations to improve the result of the proposed forecasting method. A systematic approach is proposed to improve the combination of ensemble artificial neural networks and their parameters. The proposed methodology is applied to a number of benchmark and some real life chaotic time series. In addition, the proposed forecasting method has been applied to financial sector time series, namely, the stock markets and foreign exchange rates. The experimental results confirm that the proposed method can predict the chaotic time series more effectively in terms of error indices when compared with other forecasting methods in the literature.