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

University of Heidelberg, Department of Economics, Discussion Paper No. 473

46 Pages Posted: 31 Jul 2008

See all articles by Christian Conrad

Christian Conrad

Heidelberg University - Faculty of Economics and Social Studies

Enno Mammen

University of Mannheim - Department of Economics

Date Written: July 31, 2008

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 fits 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 specifications 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 financial variables and their conditional second moments. We illustrate the usefulness of the methodology by testing the linear risk-return relation predicted by the ICAPM.

Keywords: Specification test, GARCH-M, semiparametric regression, risk premium, ICAPM

JEL Classification: C12, C14, C22, C52, G12

Suggested Citation

Conrad, Christian and Mammen, Enno, Nonparametric Regression on Latent Covariates with an Application to Semiparametric GARCH-in-Mean Models (July 31, 2008). University of Heidelberg, Department of Economics, Discussion Paper No. 473. Available at SSRN: https://ssrn.com/abstract=1192082 or http://dx.doi.org/10.2139/ssrn.1192082

Christian Conrad (Contact Author)

Heidelberg University - Faculty of Economics and Social Studies ( email )

Bergheimer Strasse 58
Heidelberg, D-69115
Germany
+49 (0)6221 54 3173 (Phone)

HOME PAGE: http://www.uni-heidelberg.de/conrad

Enno Mammen

University of Mannheim - Department of Economics ( email )

Mannheim, 68131
Germany

Register to save articles to
your library

Register

Paper statistics

Downloads
198
rank
148,458
Abstract Views
2,187
PlumX Metrics