Testing for an Omitted Multiplicative Long-Term Component in GARCH Models

Journal of Business & Economic Statistics, Forthcoming.

58 Pages Posted: 18 Jul 2015 Last revised: 15 Jun 2018

Christian Conrad

University of Heidelberg - Faculty of Economics and Social Studies

Melanie Schienle

Karlsruhe Institute of Technology (KIT)

Date Written: May 20, 2018

Abstract

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

Conrad, Christian and Schienle, Melanie, Testing for an Omitted Multiplicative Long-Term Component in GARCH Models (May 20, 2018). Journal of Business & Economic Statistics, Forthcoming.. Available at SSRN: https://ssrn.com/abstract=2631976 or http://dx.doi.org/10.2139/ssrn.2631976

Christian Conrad (Contact Author)

University of Heidelberg - Faculty of Economics and Social Studies ( email )

Bergheimer Strasse 58
Heidelberg, D-69115
Germany
+49 (0)6221 54 3173 (Phone)

HOME PAGE: http://www.uni-heidelberg.de/conrad

Melanie Schienle

Karlsruhe Institute of Technology (KIT) ( email )

Institute of Economics (ECON)
Karlsruhe
Germany

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