Volatility Forecasting and Explanatory Variables: A Tractable Bayesian Approach to Stochastic Volatility

Abstract

We provide a formulation of stochastic volatility (SV) based on Gaussian process regression (GPR). Forecasting volatility out-of-sample, both simulation and empirical analyses show that our GPR-based stochastic volatility (GPSV) model clearly outperforms SV and GARCH benchmarks, especially at long horizons. Most importantly, our approach enables the straightforward incorporation of arbitrary covariates without requiring the specification of functional forms a priori. Augmenting the GPSV model with exogenous variables increases its performance even further. In particular, a simple set of covariates reduces the error rate on one-year out-of-sample forecasting during the 2007-09 recession by 26% relative to a benchmark range-based SV model.

Keywords: Bayesian Volatility Models, Stochastic Volatility, Generalized Autoregressive Conditional Heteroscedasticity Models, Long Memory in Volatility, Multifactor Volatility

JEL Classification: C11, C22, C53