基于主成分回归的主成分个数选择实证分析

Empirical Analysis on the Choice of the Number of Principal Components Based on Principal Component Regression

针对多元线性回归模型中,自变量之间存在多重相关性问题,本文根据主成分回归原理建立模型,对主成分个数选择与模型的性能之间的关系进行了详细分析,并用沪市A股收益波动性数据进行了实证分析。结果表明:当主成分个数m增加时,模型的残差平方和S_(ES)会下降,而回归系数的均方误差M_(SE)会上升,因此m的选择应以S_(ES)和M_(SE)的变化趋势交点为宜。

For the multivariate linear regression model,there are problems of multiple correlations between variables.According to the principal component regression principle,the paper establishes the model,and analyzes in detail the relationship between the performance of the model and the number of principal components. The paper makes an empirical analysis with the data of Shanghai A stock market returns volatility. When the principal component number m increases,the model of the residual sum of squares（SES） will decrease,and the regression coefficient of the mean square error（MSE） will rise. This paper considers that the appropriate choice of m should be at the intersection of the variation trends of SES and MSE.