中文摘要：

针对证券市场指数内部结构的复杂性和影响因素的高维性，提出基于MPCA—RBF（多线性主成分分析法一径向基神经网络）模型的证券市场指数时间序列预测方法。由于证券市场间存在关联性，选取了7个证券市场及34个技术指标构建三维张量模型，采用张量方法——MPCA进行特征提取，使降维的同时充分保留数据内部结构。之后利用RBF神经网络进行回归预测，提高了预测精度。对恒生指数和日经225指数的实验结果显示，与非张量模型相比，该模型预测误差较小，预测精度有较显著的提高，表明该模型能充分地保留证券时间序列内部结构，证明了其在证券预测领域的有效性和实用性。

英文摘要：

For the complexity of internal structure and the high dimension of influencing factors of stock market index ,this paper proposed a method for time series forecasting of stock market index based on MPCA-RBF（ muhilinear principal component analysis-radial basis function） model. Due to the relationships between stock markets, this method selected seven stock markets and thirty-four stock technical indexes to construct a three-dimensional tensor model. Then, it utilized a tensor method MPCA for feature extraction of the model to preserve the internal structure of data while reducing dimension. Finally, by using RBF neural network to conduct regression prediction, the prediction accuracy was improved. Results on Hang Seng index and Nikkei 225 index closing price showed that, compared with non-tensor models, the forecast error of the proposed model was smaller and the forecasting accuracy was significantly improved. This shows that MPCA-RBF model can fully retain the internal structure of stock time series and it proves the validity and practicability of the model in field of stock forecasting.