Chaotic characteristic identification for carbon price and an multi-layer perceptron network prediction model

Dec14 and Dec15, carbon prices of European Union Emissions Trading Scheme in phase III, are studied from the chaotic point of view. Firstly, chaotic characteristics of carbon price series are identified by three classic indicators: the maximum Lyapunov exponent, the correlation dimension and the Kolmogorov entropy. Both Dec14 and Dec15 have positive maximum Lyapunov exponents, and fractal correlation dimensions and non-zero Kolmogorov entropies, which demonstrates that the fluctuant nature of carbon price can be explained as a chaotic phenomenon. The carbon price dynamic system is recovered by reconstructing the phase space. Based on phase reconstruction, an multi-layer perceptron neural network prediction model is set up for carbon price to characterize its strong nonlinearity. The logic of the MLP are described in detail. K-fold cross-validation method is applied to show the validation of the model. Four measurements in level and directional prediction are used to evaluate the performance of the MLP model. Results show the good performance of the MLP network model in predicting carbon price.