Nonparametric Independence Screening and Selection Approach for Volatility Models With Exogenous Covariates

ABSTRACT This paper introduces a nonparametric and non‐penalised variable selection procedure, called Volatility Nonparametric Independence Screening and Selection (Vol‐NIS‐S) , designed for ultra‐high‐dimensional nonlinear dynamic time series models relevant to business and industrial applications. Unlike traditional approaches, the proposed method operates without imposing parametric assumptions on the functional form linking the volatility to exogenous covariates. Assuming a zero conditional mean function, the selection mechanism relies on ranking predictors according to the correlation between the squared response and their marginal variance functions, estimated nonparametrically via kernel regression. We establish the sure screening property under mild regularity conditions. We show that the procedure can be adapted to settings with nonzero conditional mean function and to the case of heavy‐tailed innovations. Simulation studies demonstrate that Vol‐NIS‐S outperforms standard penalized regression methods, such as LASSO. The practical utility of the methodology is illustrated through an empirical analysis of Bitcoin and Gold volatility dynamics during the COVID‐19 pandemic, offering valuable insights for financial risk modeling. The empirical findings highlight substantial differences between the two assets, not only in terms of their intrinsic financial nature but also with respect to the market variables that drive their volatility dynamics.