Abstract
Symbolic regression has been utilized to infer mathematical formulas in order to solve the complex prediction and classification problems. In this paper, complex-valued S-system model (CVSS) is proposed to predict real-valued time series data. In a CVSS model, input variables and rate constants are complex-valued. The time series data need to be translated into complex numbers. The hybrid evolutionary algorithm based on complex-valued restricted additive tree and firefly algorithm is proposed to search the optimal CVSS model. Three financial time series data and Mackey–Glass chaos time series are collected to evaluate our proposed method. The experiment results show that the predicted data are very close to the target ones and our method could obtain the better RMSE, MAP, MAPE, POCID, R2, and ARV performances than ARIMA, radial basis function neural network (RBFNN), flexible neural tree (FNT), ordinary differential equation (ODE), and S-system.
Highlights
One of the main purposes of time series analysis is to predict the future data based on the existing historical one
A complex number could broaden the dimension of solution, which improves the abilities of modeling and generalization, so complex-valued methods have shown great potential for forecasting time series data [28,29,30,31,32,33,34,35]. us, this paper proposes the complex-valued version of S-system (CVSS) to solve the time series prediction problem
To search the optimal complexvalued S-system (CVSS) model, time series data need to be converted into complex data firstly
Summary
One of the main purposes of time series analysis is to predict the future data based on the existing historical one. Because the artificial neural network (ANN) has good abilities of learning, generalization, and error tolerance, many ANN models have been utilized widely to capture nonlinear characteristics for time series prediction problems in the past decades, such as radial basis function neural network (RBFNN) [10], Elman neural network [11], wavelet process neural network [12], recurrent predictor neural network (RPNN) [13], beta basis function interval type-2 fuzzy neural network [14], flexible neural tree (FNT) [15], functional link network [16], and deep neural networks [17,18]. For some practical problems, internal mechanism could not be understood from the models obtained, which may lead to restrict the problems to being solved
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