Variable selection is of great importance in high dimensional statistical modeling which nowadays appears in many areas of scientific discoveries. The main target for the variable selection is within a large scale of the variables, we need to determine those variables which play the most important roles on affecting the response, to reduce the process cost and avoid unnecessary expense. In this thesis, we give a comprehensive review of the existing variable selection methods in literature. They are the Smoothly Clipped Absolute Deviation Penalty method (SCAD), the Dantzig Selector method (DS), the Least Absolute Shrinkage and Selection Operator method (LASSO) , the Adaptive Least Absolute Shrinkage and Selection Operator method (ALASSO). By various simulation studies, we will compare the performance of the methods and point out advantages and disadvantages for each method. The main target is to use the methods to analyze the real financial database, i.e., S&P 500 index. We also will demonstrate the reason according to the theoretical results. From the result of numerical simulation, ALASSO outperforms other methods in most cases. Meanwhile, from the result of S&P 500 data analysis, LASSO performs the best among all the mentioned methods.