Semiparametric Inference in a GARCH-in-Mean Model

Publikation: Working paperForskning

  • Institut for Økonomi
A new semiparametric estimator for an empirical asset pricing model with general nonpara-
metric 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 func-
tion, 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, asymp-
totically 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 esti-
mate 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.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider47
StatusUdgivet - 2008

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