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 timevarying long-term component which is driven by the dynamics of a macroeconomic explanatory variable. We suggest a Lagrange Multiplier statistic for testing the null hypothesis that the macroeconomic variable has no explanatory power. Hence, under the null hypothesis the long-term component is constant and the GARCHMIDAS reduces to the simple GARCH model. We provide asymptotic theory for our test statistic and investigate its finite sample properties by Monte Carlo simulation. Our test statistic can be considered as an extension of the Lundbergh and Ter svirta (2002) ARCH nested in GARCH test for evaluating GARCH models. We illustrate the usefulness of our procedure by an empirical application to S&P 500 return data.
