Dimension Reduction via Penalized GLMs for Non-Gaussian Response: Application to Stock Market Volatility

We fit U.S. stock market volatilities on macroeconomic and financial market indicators and some industry level financial ratios. Stock market volatility is non-Gaussian distributed. It can be approximated by an inverse Gaussian (IG) distribution or it can be transformed by Box–Cox transformation to a Gaussian distribution. Hence, we used a Box–Cox transformed Gaussian LASSO model and an IG GLM LASSO model as dimension reduction techniques and we attempted to identify some common indicators to help us forecast stock market volatility. Via simulation, we validated the use of four models, i.e., a univariate Box–Cox transformation Gaussian LASSO model, a three-phase iterative grid search Box–Cox transformation Gaussian LASSO model, and both canonical link and optimal link IG GLM LASSO models. The latter two models assume an approximately IG distributed response. Using these four models in an empirical study, we identified three macroeconomic indicators that could help us forecast stock market volatility. These are the credit spread between the U.S. Aaa corporate bond yield and the 10-year treasury yield, the total outstanding non-revolving consumer credit, and the total outstanding non-financial corporate bonds.