股票市场数据的低维模拟

Simulations for Data of Stock Market in Low-Dimensions

摘要: 股票市场的情况是一个国家在经济上发展水平的重要参考，在分析股票市场数据时往往需要处理高维度的变量数据。直接分析这些高维度的变量数据是一件困难的工作，因此在处理这些数据时会使用降低变量维度的模拟方法来减少分析的难度。奇异值分解、因子分析和主成分回归是三种最常见的被考虑用来降低变量维度的模拟方法。为了比较这三种方法的模拟效果，本文中使用理论推导和证明的方法，得到三种方法在一定条件下有相同模拟效果的结果。于是可以得出在一定的条件下这三种降低变量维度的模拟方法具有一致性的结论。

Abstract: The situations of stock market are important references of a country’s development in economy, and we often have to deal with the high-dimensional data when we analyze those data from stock market. It’s a hard work to analyze those high-dimensional data directly, so we use the simulation methods by reducing the dimensions of variables to decrease the difficulty of analysis. SVD (Singular Value Decomposition), FA (Factor Analysis) and PCR (Principal Component Regression) are three most common simulation methods which are considered to reduce the dimensions of variables. In order to compare simulational effectiveness of the three methods, we used the method of theoretical deduction and demonstration, and got the result that the three methods had the same simulational effectiveness in some case. Hence it was able to draw the conclusion that those three methods of reducing the variable dimensions were coincident in some conditions.