GARCHX-NoVaS: A Model-free Approach to Incorporate Exogenous Variables

In this work, we explore the forecasting ability of a recently proposed normalizing and variance-stabilizing (NoVaS) transformation with the possible inclusion of exogenous variables. From an applied point-of-view, extra knowledge such as fundamentals- and sentiments-based information could be beneficial to improve the prediction accuracy of market volatility if they are incorporated into the forecasting process. In the classical approach, these models including exogenous variables are typically termed GARCHX-type models. Being a Model-free prediction method, NoVaS has generally shown more accurate, stable and robust (to misspecifications) performance than that compared to classical GARCH-type methods. This motivates us to extend this framework to the GARCHX forecasting as well. We derive the NoVaS transformation needed to include exogenous covariates and then construct the corresponding prediction procedure. We show through extensive simulation studies that bolster our claim that the NoVaS method outperforms traditional ones, especially for long-term time aggregated predictions. We also provide an interesting data analysis to exhibit how our method could possibly shed light on the role of geopolitical risks in forecasting volatility in national stock market indices for three different countries in Europe.