| We investigate bootstrap methods for nonstationary time series models. In chapter 1 we introduce some of the important ideas that we use, namely kernel regression, interval estimation, block bootstrap and the local bootstrap. In chapter 2 we develop a modified version of the block bootstrap and apply this method for interval trend estimation of nonstationary time series. In chapter 3, we apply the residual block bootstrap for interval trend estimation for the same model. In chapter 4 we consider a model that is locally stationary, where only the local block bootstrap would apply. We investigate the conditions which allow these methods to work. We develop confidence parameters of interest. We investigate the asymptotic properties of our bootstrap estimators, and their dependency on varying degrees of nonstationarity. We carry out simulations on some selected models to test the performance of these methods. |
