The Study Of Relationship Within China’s Financial Sector Based On Principal Component Analysis

In the process of analysising actual data, the principal component analysis is widely used as that the actual problem is usually multivariate. The sparse principal component analysis is a modified PCA, and this article is based on the SPCA to processing the data of Chinese financial institutions. We try to find out a reflection of actual economic changes from the view of statistics.The data used in the article comes from a variety of financial institutions in China, covering a long period of time. Since that the data is always connected with each other, we choose PCA as a powerful tool to deal with multicollinearity problem. However, PCA do has some drawbacks: the principal component of PCA usually is connected with all the varieties, and because of this, it is hard to interpret it. To overcome such drawback, we chose the SPCA, a method which could lead to sparse principal components using some penalties.Lasso is initially introduced in the field of multivariety regression to come up with sparse regression coefficients. As we transform a PCA problem to a regression problem, the application of lasso on PCA would be possible, and the principal components would be sparse. However, when the number of observations is fewer than the number of varieties, lasso could not ensure the uniqueness of results. So we then add the elastic net penalty to ensure the uniqueness of principal components, and thus, the whole sparse principal component analysis is constructed.This article first apply the SPCA on the three different parts of financial sector—banks, securities and insurances and others. After a series of comparison, we first conclude the value of several parameters in the SPCA criterion, then we apply SPCA on the data coming from different time and discuss about the trend of explained total variance. At last, we apply the SPCA on the whole data of financial sector and make some further comparison and discussion.