多元混沌时间序列的相关状态机预测模型研究

针对多元混沌时间序列预测存在的过拟合问题及高维输入变量冗余问题，提出一种新型的多变量稀疏化预测模型——多元相关状态机.该模型采用主成分分析方法对相空间重构后的高维输入变量进行低维表示，将动态储备池作为相关向量机的核函数，充分映射多元混沌时间序列的动力学特性，使得模型具有丰富的动态机制和良好的稀疏性能，有效避免过拟合问题，提高预测精度.基于两组多元混沌时间序列的仿真实验验证了模型的有效性.

Research on Multivariate Chaotic Time Series Prediction Using mRSM Model

Considering that there may be overfitting problem, as well as the problem of high dimensional redundant input variables in multivariate chaotic time series prediction, we introduce a novel multivariate prediction model based on relevance vector machine and echo state network, named multivariate relevance state machine (mRSM). The proposed model reconstructs the multivariate chaotic time series into the phase space, then reduces the dimension of input variables with the principal component analysis method. Subsequently, the mRSM uses a reservoir, replacing kernel functions of relevance vector machine, to map the dynamic features of multivariate time series sufficiently. Therefore, the mRSM presents rich dynamics and good sparsity. Furthermore, it avoids overfitting, and improves the predictive accuracy. Simulation results, based on two multivariate time series, substantiate the effectiveness of the mRSM.