| Variable selection is one of the most important topics in modern statistics and machine learning, and there are many applications on different fields. In stock market, some investors need to track certain stock market indexes for portfolio management. Unfortunately, many of indexes are complex and dynamic. So it is much more efficient for investors to apply variable selection methods in stock market index regression, which allows them to construct a simpler portfolio.This thesis reviews several methods for variable selection, among which we choose Lasso method as our modelling method. Some backgrounds, characteristics and prop-erties of Lasso method are discussed. For numerical method, we recall the Alternating Direction Method of Multipliers (ADMM), which allows the problems generated via Lasso modelling be solved efficiently, particularly for problems from big data. We test our method on sparse variable regression problem of Stock Market Index, where the stock market index which consists of about 300 stocks can be tracked via a few stocks. This is very useful in portfolio constructing, arbitrage trading and other hedging strate-gies. By analysing the regression results, not only the characteristics and properties of these methods are verified, but also a new idea of arbitrage trading strategy is proposed. |
