中文摘要：

由于金融时间序列具有非线性的特点，经典的Sharpe模型难以全面、准确地描述经济变量之间的关系。为此，提出了基于谱映射的非线性Sharpe模型。谱映射的核心思想来源于经典的谱图理论。谱映射借助由数据集导出的一些特殊矩阵的部分特征向量，将该数据集投影至高维空间。在投影后的高维空间，数据集的有些性质得到改进，如原空间中线性不可分的数据集在高维空间线性可分。基于谱映射的非线性Sharpe模型，利用谱映射将基金收益率数据和风格指数收益率数据投影至高维空间，在高维空间利用经典Sharpe模型识别各基金的投资风格。利用基于谱映射的非线性Sharpe模型分析了部分开放式基金的投资风格。实验结果表明，本文提出的基于谱映射的非线性Sharpe模型的性能优于在原数据集上直接利用经典Sharpe模型得到的结果。

英文摘要：

Because of nonlinearity of financial time series, classical Sharpe model often fails to reflect the relations among the economic factors accurately. Therefore, we propose a nonlinear Sharpe model based on spectral mapping. Spectral mapping is derived from spectral graph theory, and utilizes parts of eigenvectors of some special matrices, constructed according to the original dataset, to map the original data to high dimensional space. In the high dimensional space, some properties of the dataset is improved. For example, the mapped dataset in the high dimensional space can be linear separable, which is not linear separable in the original space. Nonlinear Sharpe model based on spectral mapping consists of the following steps. Firstly, returns of the funds and investment styles are mapped to high dimensional space- Secondly, classical Sharpe model is used to recognize investment styles in the high dimensional space. Nonlinear Sharpe model based on spectral mapping is used to recognize investment styles of some open-end funds. Experimental results show that, the performance of nonlinear Sharpe model based on spectral mapping outperforms the classical Sharpe model in the original dataset.