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

Tao Li,Thanasis Stengos,Anthony F Desmond

doi:10.3390/jrfm14120583

Abstract

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.

Highlights

IntroductionAs well as financial industry studies, have focused on studying the strong persistence pattern of volatility time series data, described by volatility clustering and long memory
We find that the optimal power of the link function for the inverse Gaussian (IG) GLM least absolute shrinkage and selection operator (LASSO) model is close to the optimal Box–Cox transformation parameter λBC, i.e., around true parameter −0.5, which means the latter can provide us with a good clue for a better link function
We explored the distribution of stock market volatility data using low frequency quarterly series, which are stationary after first order differencing

Summary

Introduction

As well as financial industry studies, have focused on studying the strong persistence pattern of volatility time series data, described by volatility clustering and long memory. These two patterns are well captured by Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models and Fractionally Integrated Generalized AutoRegressive Conditionally Heteroskedastic (FIGARCH) models, respectively. The FIGARCH model was first introduced in Baillie et al (1996) to capture the slow hyperbolic rate of decay of the influence of lagged squared innovations in the time series of the conditional variance of Deutsch Mark–U.S.Dollar exchange rates Both the GARCH and the FIGARCH models capture the volatility persistence pattern very well. In the appendix we present some computational algorithms that were used in the analysis

Methods

Results

Conclusion