Time-series forecasting by means of linear and nonlinear models

Abstract

The main objective of this paper is two folds. First is to assess some well-known linear and nonlinear techniques comparatively in modeling and forecasting financial time series with trend and seasonal patterns. Then to investigate the effect of pre-processing procedures, such as seasonal adjustment methods, to the improvement of the modeling capability of a nonlinear structure implemented as ANNs in comparison to the classical Box-Jenkins seasonal autoregressive integrated moving average (ARIMA) model, which is widely used as a linear statistical time series forecasting method. Furthermore, the effectiveness of seasonal adjustment procedures, i.e. direct or indirect adjustments, on the forecasting performance is evaluated. The Autocorrelation Function (ACF) plots are used to determine the correlation between lags due to seasonality, and to determine the number of input nodes that is also confirmed by trial-and-errors. The linear and nonlinear models mentioned above are applied to aggregate retail sales data, which carries strong trend and seasonal patterns. Although, the results without any pre-processing were in an acceptable interval, the overall forecasting performance of ANN was not better than that of the classical method. After employing the right seasonal adjustment procedure, ANN has outperformed its linear counterpart in out-of-sample forecasting. Consequently, it is confirmed that the modeling capability of ANN is improved significantly by using a pre-processing procedure. The results obtained from both ARIMA and ANNs based forecasting methodologies are analyzed and compared with Mann-Whitney statistical test.