Semiparametric Multiplicative GARCH-X Model: Adopting Economic Variables To Explain Volatility

Abstract

This paper investigates a multiplicative GARCH-X model, which has a nonparametric long run component induced by an exogenous covariate and a GARCH short run component. Compared to the usual additive GARCH-X model that includes an additional exogenous covariate in the GARCH model, this model contains a nonlinear function of an exogenous covariate that is multiplied to the GARCH model. When the covariate is nonstationary, i.e. integrated or near-integrated, the model can explain various stylized facts of financial time series. We suggest a kernel-based estimation procedure for the parametric and nonparametric components and derive related asymptotic properties. The asymptotic analysis is non-standard when the included covariates are non-stationary, and involves novel techiques for nonparametric and semiparametric estimation. An empirical application studies the linkage between US and European stock market volatilities using the VIX index as a covariate in our multiplicative GARCH-X model. It is shown that the model outperforms standard models both in terms of in-sample fitting and out-of-sample forecasting.