基于相空间重构的混合神经网络对金融混沌序列预测研究

Chaotic Financial Series Prediction Study Based on Hybrid Model with Neural Network and Reconstructing Phase Space

摘要: 应用相空间延迟重构技术重构出2010年至2019年上证指数变动序列的奇异吸引子，并计算得出其最大Lyapunov指数为正，从而验证了上证指数序列的混沌特性；利用虚假邻域法确定恰当的嵌入空间维数应用于遗传神经网络并和高斯核权局部预测构造混合预测算法，实现对奇异吸引子中运动轨道的估计，从而达到对该混沌序列的预测。实证表明：与常用的循环神经网络方法相比，该技术显著提高了学习效率和预测精度。

Abstract: Strange attractor of Shanghai Stock Index series from 2010 to 2019 is reconstructed by the method of reconstructing phase space, then shows that the largest exponent of Lyapunov is positive through numerical simulation, which confirms that the index series is chaotic. The optimum embedding dimensionality is selected by method of false neighbors. On this basis, a hybrid prediction model based on neural network with genetic algorithm and local forecasting with Gaussian Kernel is proposed, which can forecast chaotic series by estimating the trajectory of strange attractor. Compared with RNN, this prediction model has better convergence speed and prediction accuracy.