Semi-parametric estimation and forecasting for exogenous log-GARCH models

Advanced computing and processing techniques have yielded abundant information for financial time series forecasting. It is, therefore, natural to ask for possible extensions of time series models to accommodate the wealth of information. In this article, we develop a new model for financial volatility estimation and forecasting by incorporating exogenous covariates in a semi-parametric log-GARCH model. With additional information, we gain an increased prediction power. We propose a quasi-maximum likelihood procedure via spline smoothing technique. Consistent estimators and asymptotic normality are obtained under mild regularity conditions. Simulation experiments provide strong evidence that corroborates the asymptotic theories. Additionally, an application to SPY index data demonstrates strong competitive advantage of our model comparing with GARCH(1,1) and log-GARCH(1,1) models.