Inference of time series regression models with weakly dependent errors

In this thesis we develop inferential methods for time series models with weakly dependent errors in the following three aspects. The first aspect concerns the issue of the size-distortion in the presence of strong temporal dependence, which is well-known in the literature. There are recently proposed bandwidth-free methods, which generally reduces the size-distortion compared to the traditional method. However, these methods still suffer from severe size distortion when the temporal dependence in the error process is strong. We propose to use the prewhitening to handle the strong temporal dependence so that the size distortion is greatly reduced in the presence of strong temporal dependence in the error. This work is presented as Chapter 2, in the context of time series regression with dynamic regressors and stationary and weakly dependent errors. The second and third aspects are motivated by the recent surge of awareness that the stationarity assumption for the error is often too restrictive for real data. Some macroeconomic series are often observed to have heteroscedastic behavior. In Chapter 3, we introduce short-memory nonstationary error framework that can accommodate a wide range of nonstationary linear processes or modulated stationary processes in the context of trend assessment setting. We propose a method that can handle both heteroscedastic behavior and the temporal dependence in the error process. In Chapter 4, we further introduce a piecewise locally stationary framework for the error process that can cover a wide range of linear and nonlinear processes that are short-memory nonstationary in the unit root setting. A bootstrap-based method is proposed and its consistency is proved