In ﬁnancial time series nonlinear eﬀects and time-varying eﬀects are observed. In this dissertation we propose a predictive regression model with time varying coeﬃcients and functional coeﬃcients. It allows for nonstationary predictors. We establish asymptotics for the coeﬃcient estimation and show oracle properties of the resulting estimators under stationary and nonstationary settings. Simulations demonstrate good ﬁnite sample performance of our estimators. A real example illustrates the use of our methodology.