Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system

Identifying parameters of financial and economic models with chaotic dynamics is an important, yet daunting challenge because of the complexities there exist in these chaotic systems. Although several studies have been devoted to understanding the mechanism of financial systems, the application of most state-of-the-art methods to these systems is completely ignored. To the best of our knowledge, no study identifies and predicts fractional derivatives of economic models. The current study has been motivated by this issue. Employing the Differential Evolution algorithm, Gaussian process regression, and neural networks, we propose a novel algorithm to identify and predict parameters of a symmetric chaotic fractional financial model. In the first step, a combination of Differential Evolution and the Gaussian process is utilized to identify time-varying fractional-order derivatives. Then, through numerical simulation, it is demonstrated that although this method provides bright results for estimation and interpolation purposes, it fails to extrapolate and predict time-varying parameters. Hence, in the next step, by taking advantage of a recurrent neural network, the proposed method is promoted and modified for extrapolation. Numerical simulations firmly confirm the excellent performance of the improved algorithm for both interpolation and extrapolation purposes.