  Seasonality is a distinctive characteristic which is often observed in many
practical time series. Artificial Neural Networks (ANNs) are a class of
promising models for efficiently recognizing and forecasting seasonal patterns.
In this paper, the Particle Swarm Optimization (PSO) approach is used to
enhance the forecasting strengths of feedforward ANN (FANN) as well as Elman
ANN (EANN) models for seasonal data. Three widely popular versions of the basic
PSO algorithm, viz. Trelea-I, Trelea-II and Clerc-Type1 are considered here.
The empirical analysis is conducted on three real-world seasonal time series.
Results clearly show that each version of the PSO algorithm achieves notably
better forecasting accuracies than the standard Backpropagation (BP) training
method for both FANN and EANN models. The neural network forecasting results
are also compared with those from the three traditional statistical models,
viz. Seasonal Autoregressive Integrated Moving Average (SARIMA), Holt-Winters
(HW) and Support Vector Machine (SVM). The comparison demonstrates that both
PSO and BP based neural networks outperform SARIMA, HW and SVM models for all
three time series datasets. The forecasting performances of ANNs are further
improved through combining the outputs from the three PSO based models.
