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Nonparametric Regression on Latent Covariates with an Application to Semiparametric GARCH-in-Mean Models

  • Christian Conrad

    ()

    (University of Heidelberg, Department of Economics)

  • Enno Mammen

    ()

    (University of Mannheim, Department of Economics)

We consider time series models in which the conditional mean of the response variable given the past depends on latent covariates. We assume that the covariates can be estimated consistently and use an iterative nonparametric kernel smoothing procedure for estimating the conditional mean function. The covariates are assumed to depend (non)parametrically on past values of the covariates and of the observations. Our procedure is based on iterative ¯ts of the covariates and nonparametric kernel smoothing of the conditional mean function. An asymptotic theory for the resulting kernel estimator is developed and the estimator is used for testing parametric speci¯cations of the mean function. Our leading example is a semiparametric class of GARCH-in-Mean models. In this set-up our procedure provides a formal framework for testing economic theories that postulate functional relations between macroeconomic or ¯nancial variables and their conditional second moments. We illustrate the usefulness of the methodology by testing the linear risk-return relation predicted by the ICAPM.

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File URL: http://www.uni-heidelberg.de/md/awi/forschung/dp473.pdf
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Paper provided by University of Heidelberg, Department of Economics in its series Working Papers with number 0473.

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Length: 45 pages
Date of creation: Jul 2008
Date of revision: Jul 2008
Handle: RePEc:awi:wpaper:0473
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