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.

考虑随时间变化的过程具有误差的线性回归模型。在这类模型中，趋势函数和误差项的相关结构中的平滑性条件确保了可以通过平稳过程对这些模型进行局部逼近，从而得到具有局部平稳误差的一类线性回归模型。在此，我们将重点放在此类回归模型的最小二乘估计量分布的自举近似上。我们通过深入的模拟研究比较和讨论了经典和自举置信区间的结果。还通过对具有局部平稳误差的美国每月通货膨胀时间序列的真实数据分析来讨论这种趋势。