Semiparametric Inference in a GARCH-in-Mean Model

CREATES Research Paper No. 2008-46

49 Pages Posted: 2 Sep 2008

See all articles by Bent Jesper Christensen

Bent Jesper Christensen

Aarhus University; Aarhus University; Aarhus University

Christian M. Dahl

Department of Business and Economics

Emma M. Iglesias

Michigan State University

Date Written: September 2, 2008

Abstract

A new semiparametric estimator for an empirical asset pricing model with general nonparametric risk-return tradeoff and a GARCH process for the underlying volatility is introduced. The estimator does not rely on any initial parametric estimator of the conditional mean function, and this feature facilitates the derivation of asymptotic theory under possible nonlinearity of unspecified form of the risk-return tradeoff. Besides the nonlinear GARCH-in-mean effect, our specification accommodates exogenous regressors that are typically used as conditioning variables entering linearly in the mean equation, such as the dividend yield. Using the profile likelihood approach, we show that our estimator under stated conditions is consistent, asymptotically normal, and efficient, i.e. it achieves the semiparametric lower bound. A sampling experiment provides evidence on finite sample properties as well as comparisons with the fully parametric approach and the iterative semiparametric approach using a parametric initial estimate proposed by Conrad and Mammen (2008). An empirical application to the daily S&P 500 stock market returns suggests that the linear relation between conditional expected return and conditional variance of returns from the literature is misspecified, and this could be the reason for the disagreement on the sign of the relation.

Keywords: Efficiency bound, GARCH-M model, Profile likelihood, Risk-return relation, Semiparametric inference

JEL Classification: C13, C14, C22, G12

Suggested Citation

Christensen, Bent Jesper and Dahl, Christian M. and Iglesias, Emma M., Semiparametric Inference in a GARCH-in-Mean Model (September 2, 2008). CREATES Research Paper No. 2008-46. Available at SSRN: https://ssrn.com/abstract=1262230 or http://dx.doi.org/10.2139/ssrn.1262230

Bent Jesper Christensen (Contact Author)

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210
Denmark

Christian M. Dahl

Department of Business and Economics ( email )

Campusvej 55
DK-5230 Odense M
Denmark
29125486 (Phone)

Emma M. Iglesias

Michigan State University

Agriculture Hall
East Lansing, MI 48824-1122
United States

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