Asymptotics for Parametric GARCH-in-Mean Models

Journal of Econometrics, Forthcoming

26 Pages Posted: 10 Feb 2015 Last revised: 3 Jan 2017

See all articles by Christian Conrad

Christian Conrad

Heidelberg University - Alfred Weber Institute for Economics; ETH Zürich - KOF Swiss Economic Institute

Enno Mammen

University of Mannheim - Department of Economics

Date Written: February 2, 2016

Abstract

In this paper we develop an asymptotic theory for the Quasi-Maximum Likelihood Estimator (QMLE) of the parametric GARCH-in-Mean model. The asymptotics is based on a study of the volatility as a process of the model parameters. The proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem. Our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model. Nevertheless, our theory does not yet treat all standard specifications of the mean function.

Keywords: GARCH-in-Mean, stochastic recurrence equations, risk-return relationship

JEL Classification: C13, C22, C51, G12

Suggested Citation

Conrad, Christian and Mammen, Enno, Asymptotics for Parametric GARCH-in-Mean Models (February 2, 2016). Journal of Econometrics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=2562270 or http://dx.doi.org/10.2139/ssrn.2562270

Christian Conrad (Contact Author)

Heidelberg University - Alfred Weber Institute for Economics ( email )

Grabengasse 14
Heidelberg, D-69117
Germany
+49 (06)221 543173 (Phone)

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

ETH Zürich - KOF Swiss Economic Institute ( email )

Zurich
Switzerland

Enno Mammen

University of Mannheim - Department of Economics ( email )

Mannheim, 68131
Germany

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