Semiparametric model building for regression models with time-varying parameters

This paper considers the problem of semiparametric model building for linear regression models with potentially time-varying coefficients. By allowing the response variable and explanatory variables be jointly a nonstationary process, the proposed methods are widely applicable to nonstationary and dependent observations. We propose a local linear shrinkage method that can simultaneously achieve parameter estimation and variable selection. Its selection consistency and the favorable oracle property are established. Due to the fear of losing efficiency, an information criterion is further proposed for distinguishing between time-varying and time-constant components. Numerical examples are presented to illustrate the proposed methods.