Misspecification testing in GARCH-MIDAS models

We develop a misspecification test for the multiplicative two-component GARCH-MIDAS model suggested in Engle et al. (2013). In the GARCH-MIDAS model a short-term unit variance GARCH component fluctuates around a smoothly time-varying long-term component which is driven by the dynamics of an explanatory variable. We suggest a Lagrange Multiplier statistic for testing the null hypothesis that the variable has no explanatory power. Hence, under the null hypothesis the long-term component is constant and the GARCH-MIDAS reduces to the simple GARCH model. We derive the asymptotic theory for our test statistic and investigate its finite sample properties by Monte-Carlo simulation. The usefulness of our procedure is illustrated by an empirical application to S&P 500 return data.