Partial time-varying regression modelling under general heterogeneity

This paper explores a semiparametric version of a time-varying regression, where a subset of the regressors have a fixed coefficient and the rest a time-varying one. We provide an estimation method and establish associated theoretical properties of the estimates and standard errors in extended for heterogeneity regression space. In particular, we show that the estimator of the fixed regression coefficient preserves the parametric rate of convergence, and that, despite of general heterogenous environment, the asymptotic normality property for components of regression parameters can be established and the estimators of standard errors have the same form as those given by White (1980). The theoretical properties of the estimator and good finite sample performance are confirmed by Monte Carlo experiments and illustrated by an empirical example on forecasting.