Real-world time series such as econometric time series are rarely linear and they have characteristics of volatility. Although autoregressive conditional heteroscedasticity models have used for forecasting financial time series, these models are specific models for time series, so they are not generally applied for all-time series. ARCH–GARCH models usually applied on financial time series. Because, since these time series include features like volatility clustering and leptokurtic and therefore cause problem of heteroscedastic. These problems can be handled thanks to these models. However, These model can be modelled by ARCH–GARCH models only if they include arch effect after being checked that whether ARCH effect exists or not. Therefore, in recent years artificial neural networks have been commonly used various fields by many researchers for any nonlinear-or linear time series, especially multiplicative neuron model-based artificial neural networks are commonly used that have successful forecasting results. It is known that hybrid methods in artificial neural networks are useful techniques for forecasting time series. In this study, a new hybrid forecasting method has a multiplicative neural network structure AR–ARCH–ANN model has been proposed. The proposed method is a recurrent model and also it can model volatility with having autoregressive conditional heteroscedasticity structure. In the proposed approach, particle swarm optimization is used for training neural network. Possibilities of avoiding local minimum traps are increased by this algorithm in using trained process. Istanbul Stock Exchange daily data sets from 2011 to 2013 and some time series in using for 2016 International Time Series Forecasting Competition are obtained to evaluate the forecasting performance of AR–ARCH–ANN. Then, results produced by the proposed method were compared with other methods and it has better performance from other methods.