Effectiveness of PSO Based Neural Network for Seasonal Time Series Forecasting R. Adhikari and R.K. Agrawal School of Computer and Systems Sciences, Jawaharlal Nehru University, New Delhi-110067, India {adhikari.ratan,rkajnu}@gmail.com Abstract. Recently, the Particle Swarm Optimization (PSO) technique has gained much attention in the field of time series forecasting. Although PSO trained Artificial Neural Networks (ANNs) performed reasonably well in stationary time series forecasting, their effectiveness in track- ing the structure of non-stationary data (especially those which contain trends or seasonal patterns) is yet to be justified. In this paper, we have trained neural networks with two types of PSO (Trelea1 and Trelea2) for forecasting seasonal time series data. To assess their performances, experiments are conducted on three well-known real world seasonal time series. Obtained forecast errors in terms of three common performance measures, viz. MSE, MAE and MAPE for each dataset are compared with those obtained by the Seasonal ANN (SANN) model, trained with a standard backpropagation algorithm. Comparisons demonstrate that training with PSO-Trelea1 and PSO-Trelea2 produced significantly bet- ter results than the standard backpropagation rule. Keywords: Particle Swarm Optimization, Evolutionary Computation, Time Series Forecasting, ANN, Seasonal ANN. 1 Introduction Time series forecasting is a dynamic research area which has important applica- tions in various practical decision making situations. In time series forecasting, the past observations are carefully collected and rigorously studied to develop an appropriate model which in turn is used to generate future values for the series. Thus time series forecasting can be termed as the act of predicting the future by understanding the past. The most popular statistical techniques used for fore- casting are the Box-Jenkins or ARIMA models [1]. Although these models can represent several varieties of time series with ease and simplicity, they make the presumption that the associated series is linear in nature. This imposed restric- tion makes them inadequate in many practical situations, as most of the real world time series are generated from non-linear processes [2]. To overcome this drawback, various non-linear statistical models have been proposed in literature. Some of them are: the Autoregressive Conditional Heteroskedasticity (ARCH) model [2, 3], the Generalized ARCH (GARCH) [2, 4] and the Exponential Gen- eralized ARCH (EGARCH) [4], the Threshold Autoregressive (TAR) model [5], Proceedings of the Fifth Indian International Conference on Artificial Intelligence 231