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

We consider time series models in which the conditional mean of the response variable given thepast depends on latent covariates. We assume that the covariates can be estimated consistentlyand use an iterative nonparametric kernel smoothing procedure for estimating the conditional meanfunction. The covariates are assumed to depend (non)parametrically on past values of the covariatesand of the observations. Our procedure is based on iterative fits of the covariates and nonparametrickernel smoothing of the conditional mean function. An asymptotic theory for the resulting kernelestimator is developed and the estimator is used for testing parametric specifications of the meanfunction. Our leading example is a semiparametric class of GARCH-in-Mean models. In this set-upour procedure provides a formal framework for testing economic theories that postulate functionalrelations between macroeconomic or financial variables and their conditional second moments. Weillustrate the usefulness of the methodology by testing the linear risk-return relation predicted by theICAPM.[...]