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中文摘要：
本文将追踪误差定义为股票投资组合收益率与所追踪指数的基准收益率之差，分别在无交易费用和有交易费用的情况下，建立追踪误差极小化的股票指数预测模型．首先采用稀疏主成分分析法对沪深300以及香港恒生的股票进行选择，然后根据所选择的股票样本求解股票指数预测模型．数值实验表明基于稀疏主成分的股票指数追踪模型具有稀疏性、可解释性及较好的样本外追踪误差的优点．
英文摘要：
In this paper, the tracking error is defined as the absolute deviations of the return ratio of portfolio to that of the tracking-index benchmark and then the forecasting model for stock index is established by minimizing tracking-error in transaction cost and no transaction cost case respectively. Firstly, the sparse principal component analysis method （SPCA） is applied to select the stocks from HuShen 300 and Hang Seng, then we obtain a good prediction for the stock index by the model. The extensive experiments demonstrate that the SPCA-basedforecasting model for stock index has sparsity, good interpretability and better projection of tracking error.
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