Forecasting nonlinear time series with a hybrid methodology

Applied Mathematics Letters (Impact Factor: 1.5). 01/2009; 22:1467-1470. DOI:10.1016/j.aml.2009.02.006
Source: DBLP

ABSTRACT a b s t r a c t In recent years, artificial neural networks (ANNs) have been used for forecasting in time series in the literature. Although it is possible to model both linear and nonlinear structures in time series by using ANNs, they are not able to handle both structures equally well. Therefore, the hybrid methodology combining ARIMA and ANN models have been used in the literature. In this study, a new hybrid approach combining Elman's Recurrent Neural Networks (ERNN) and ARIMA models is proposed. The proposed hybrid approach is applied to Canadian Lynx data and it is found that the proposed approach has the best forecasting accuracy.

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    ABSTRACT: 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.
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