A new linear & nonlinear artificial neural network model for time series forecasting

Artificial neural network approach is a well-known method that is a useful tool for time series forecasting. Since real life time series can generally contain both linear and nonlinear components, hybrid approaches which can model both these two components have also been proposed in the literature. The hybrid approaches suggested in the literature generally have two phases. In the first phase, linear component of time series is modeled with a linear model. Then, nonlinear component is modeled by utilizing a nonlinear model in the second phase. In two-phase methods, it is assumed that time series has only a linear structure in the first phase. Also, it is assumed that time series has only a nonlinear structure in the second phase. Therefore, this causes model specification error. In order to overcome this problem, a novel neural network model, which consists of both linear and nonlinear structures, is proposed in this study. The proposed model considers that time series has both linear and nonlinear components. Multiplicative and Mc Culloch-Pitts neuron structures are employed for nonlinear and linear parts of the proposed model, respectively. In addition, the modified particle swarm optimization method is used to train the proposed neural network model. In order to show the performance of the proposed approach, it is applied to three real life time series and obtained results are compared to those obtained from other approaches available in the literature. It is observed that the proposed model gives the best forecasts for these three time series

Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations

A given observation in time series does not only depend on preceding one but also previous ones in general. Therefore, high order fuzzy time series approach might obtain better forecasts than does first order fuzzy time series approach. Defining fuzzy relation in high order fuzzy time series approach are more complicated than that in first order fuzzy time series approach. A new proposed approach, which uses feed forward neural networks to define fuzzy relation in high order fuzzy time series, is introduced in this paper. The new proposed approach is applied to well-known enrollment data for the University of Alabama and obtained results are compared with other methods proposed in the literature. It is found that the proposed method produces better forecasts than the other methods

A new approach for determining the length of intervals for fuzzy time series

In the implementations of fuzzy time series forecasting, the identification of interval lengths has an important impact on the performance of the procedure. However, the interval length has been chosen arbitrarily in many papers. Huarng developed a new approach which is called ratio-based lengths of intervals in order to identify the length of intervals. In our paper, we propose a new approach which uses a single-variable constrained optimization to determine the ratio for the length of intervals. The proposed approach is applied to the two well-known time series, which are enrollment data at The University of Alabama and inventory demand data. The obtained results are compared to those of other methods. The proposed method produces more accurate predictions for the future values of used time series