Time-Varying Volatility Persistence in a GARCH-MIDAS Framework

This paper presents a new volatility model with time-varying volatility persistence (TVP) that is governed by the dynamics of an explanatory variable. We extend the GJR-GARCH model by introducing a time-varying GARCH coefficient that is linked to the variable in a parsimonious way using MIDAS techniques. We refer to the model as the TVP-GARCH-MIDAS model. It nests the GJR-GARCH under the null that the variable has no explanatory power. We present a misspecification test based on the Lagrange multiplier principle and study its finite sample properties in a Monte-Carlo simulation. In an empirical application to the U.S. stock market, we show that volatility persistence is positively related to realized volatility and that it varies across the business cycle in a counter cyclical way. Finally, we assess forecasting gains of the new model in a direct forecasting comparison.