Nonparametric Regression with a Latent Time Series

In this paper we investigate a class of semiparametric models for panel datasetswhere the cross-section and time dimensions are large. Our model contains alatent time series that is to be estimated and perhaps forecasted along with anonparametric covariate effect. Our model is motivated by the need to be flexiblewith regard to functional form of covariate effects but also the need to be practicalwith regard to forecasting of time series effects. We propose estimation proceduresbased on local linear kernel smoothing; our estimators are all explicitly given. Weestablish the pointwise consistency and asymptotic normality of our estimators. Wealso show that the effects of estimating the latent time series can be ignored incertain cases.