Semiparametric Inference in a GARCH-in-Mean Model

    Research output: Working paper/Preprint Working paperResearch

    Abstract

    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.
    Original languageEnglish
    Place of publicationAarhus
    PublisherInstitut for Økonomi, Aarhus Universitet
    Number of pages47
    Publication statusPublished - 2008

    Keywords

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

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