Testing for an Omitted Multiplicative Long-Term Component in GARCH Models
Updated version of: University of Heidelberg, Department of Economics, Discussion Paper No. 597
53 Pages Posted: 18 Jul 2015 Last revised: 25 Jan 2018
Date Written: January 24, 2018
We consider the problem of testing for an omitted multiplicative long-term component in a simple GARCH model. Under the alternative there is a two-component model with a short-term GARCH component that 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. We derive the asymptotic theory for our test statistic and investigate its finite sample properties by Monte-Carlo simulation. Our test also covers the mixed-frequency case in which the returns are observed at a higher frequency than the explanatory variable. The usefulness of our procedure is illustrated by empirical applications to S&P 500 return data.
Keywords: GARCH-MIDAS, LM test, Long-term Volatility, Volatility Component Models
JEL Classification: C53, C58, E32, G12
Suggested Citation: Suggested Citation