Estimation for Nonlinear Times Series Models with Stationary and Non-stationary Regressors

This thesis aims to propose better models to deal with non-stationary time series since they pose a major challenge for modelling and accurate forecasting. Chapter 2 considers a nonlinear cointegrating model with a mixture of time-varying and non-time-varying coefficients to explain the relationship between tax benefits and fertility rate. Chapter 3 proposes a parametric nonlinear single-index predictive model; Chapter 4 extends the model in Chapter 3 by allowing for lagged dependent variables. In the case of stock return predictability, we find that models in Chapter 3 and 4 produce better out-of-sample fits than the commonly used benchmark models.