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This book presents a new model of neural network for time series analysis and forecasting: the ARMA-CIGMN (Autoregressive Moving Average Classical Incremental Gaussian Mixture Network) model and its analysis. This model is based on modifications made to a reformulated IGMN, the Classical IGMN (CIGMN). The CIGMN is similar to the original IGMN, but based on a classical statistical approach. The modifications to the IGMN algorithm were made to better fit it to time series. The ARMA-CIGMN model demonstrates good forecasts and the modeling procedure can also be aided by known statistical tools as the autocorrelation (acf) and partial autocorrelation functions (pacf), already used in classical statistical time series modeling and also with the original IGMN algorithm models. The ARMA-CIGMN model was evaluated using known series and simulated data.