Bootstrapping regression models with locally stationary disturbances

A linear regression model with errors following a time-varying process is considered. In this class of models, the smoothness condition both in the trend function and in the correlation structure of the error term ensures that these models can be locally approximated by stationary processes, leading to a general class of linear regression models with locally stationary errors. We focus here on the bootstrap approximation to the distribution of the least-squares estimator for such class of regression models. We compare and discuss the results on both the classical and bootstrap confidence intervals through an intensive simulation study. The trend is also discussed through a real data analysis on time series of monthly inflation in US with locally stationary errors.