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

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  • Christian Conrad

    ()
    (University of Heidelberg, Department of Economics)

  • Enno Mammen

    ()
    (University of Mannheim, Department of Economics)

Abstract

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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Bibliographic Info

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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Keywords: Speci¯cation test; GARCH-M; semiparametric regression; risk premium; ICAPM.;

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Citations

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Cited by:
  1. Bent Jesper Christensen & Morten Ørregaard Nielsen & Jie Zhu, 2007. "Long Memory in Stock Market Volatility and the Volatility-in-Mean Effect: The FIEGARCH-M Model," CREATES Research Papers 2007-10, School of Economics and Management, University of Aarhus.
  2. Conrad, Christian & Loch, Karin, 2012. "Anticipating Long-Term Stock Market Volatility," Working Papers 0535, University of Heidelberg, Department of Economics.
  3. Christensen, Bent Jesper & Dahl, Christian M. & Iglesias, Emma M., 2012. "Semiparametric inference in a GARCH-in-mean model," Journal of Econometrics, Elsevier, vol. 167(2), pages 458-472.

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