Time series forecasting is an active research area that has drawn considerable attention for applications in a variety of areas. Forecasting accuracy is one of the most important features of forecasting models. Nowadays, despite the numerous time series forecasting models which have been proposed in several past decades, it is widely recognized that financial markets are extremely difficult to forecast. Artificial Neural Networks (ANNs) are flexible computing frameworks and universal approximators that can be applied to a wide range of forecasting problems with a high degree of accuracy. However, using ANNs to model linear problems have yielded mixed results, and hence; it is not wise to apply them blindly to any type of data. Improving forecasting especially time series forecasting accuracy is an important yet often difficult task facing decision makers in many areas. Both theoretical and empirical findings have suggested that integration of different models can be an effective method of improving upon their predictive performance, especially when the models in the ensemble are quite different.
This is the reason that hybrid methodologies combining the linear models such as ARIMA and nonlinear models such as ANNs have been proposed in the literature of time series forecasting. These hybrid techniques decompose a time series into its linear and nonlinear form in order to use the unique advantages of linear and nonlinear modeling methods and are one of the most popular hybrid models, which have recently been shown to be successful for single models. In this paper, an improved version of the hybrid ANNs/ARIMA models is proposed for time series forecasting. In the proposed model, the performance of the hybrid ANNs/ARIMA models is improved using diagnosing the trend of residuals by Probabilistic Neural Networks (PNNs). Empirical results of exchange rate forecasting indicate that the proposed model is more satisfactory than ANNs/ARIMA models.