中文摘要：

目前基于核主成分分析方法（KPCA）以及支持向量机（SVM）的财务危机预警模型中,所使用的核函数基本都是单核函数。混合核函数能够充分利用不同核函数的特征映射能力,在处理非线性关系时较单核函数具有更优越的性能。基于双正交小波在非线性信号处理方面的良好性能,构造了一类新的双正交小波核函数并证明其满足正定核的容许性条件,在此基础上,构造了新的双正交小波混合核函数。提出了基于双正交小波混合核函数的KPCA-SVM财务危机预警模型,并以我国证券市场上市公司为对象进行实证研究。结果表明,所构造的双正交小波混合核函数能够有效改进KPCA的特征提取性能并提高SVM模型的预测精度,显著改善了财务危机预警精度。

英文摘要：

Financial crisis prediction is generally studied using the kernel principal component analysis （KPCA） and support vector machine （SVM） model. However, the kernel function used in these methods is basically single kernel function. Actually, hybrid kernel is superior to the component kernels in dealing with non-linear issues, for it can make full use of their different feature mapping abilities. In view of the excellent performance of biorthogonal wavelet in nonlinear signal processing, a new type of biorthogonal wavelet kernel function is constructed and proved to be valid due to the satisfaction of the admissibility conditions of the positive definite kernel. In addition, biorthogonal wavelet hybrid kernel function is constructed and KPCA-SVM model for financial crisis prediction based on biorthogonal wavelet hybrid kernel function is also proposed. The empirical study on the listed companies in China~s securities market is conducted. The results show that the biorthogonal wavelet hybrid kernel function constructed can effectively improve the feature extraction performance in KPCA and enhance the prediction accuracy of SVM model to a great degree, hence the accuracy of the financial crisis prediction is thus significantly improved.