A new adaptive variable selection criterion and its applications in financial markets

This thesis is targeting on proposing a new variable selection method and showing its applications in financial markets. Statistically, this thesis constructs a new adaptive variable selection criterion, proves its same asymptotic rate with mini-max estimator, and shows its effectiveness in simulation. In its finance applications, it measures news articles by keyword frequencies, finds the lack of prediction power from news, and discovers that price variation of stocks are mostly idiosyncratic. This thesis consists of three parts. The first part develops a new adaptive criterion for variable selection and estimation in prediction problems. As opposed to traditional fixed dimensionality penalty criteria (AIC, Cp, BIC, and RIC), the proposed procedure adjusts the penalty corresponding with the data. Both an asymptotic analysis and a simulation show the effectiveness of this new method. The second part of this thesis models the effects of business news releases on the stock market. We define thousands of keyword frequency variables from Reuters' news articles and build regression models to explore their connections with contemporaneous and subsequent stock market activities. After including necessary financial factors, several frequency variables are found statistically significant for explaining market activities while few are found valuable for predicting. In the final part of this thesis, R's are calculated for the returns of large stocks as explained by the overall market factor, by the Fama-rench factors, and by the returns on other stocks. With daily data, the average out-of-sample R2 is only .17 by the market factor, .21 by the Fama-French factors, and .32 by the returns on other stocks. This result suggests that stock price changes of large firms are more influenced by their individual events or characteristics.