Time Series Regression Models with Locally Stationary Disturbance

Time series linear regression model with the stationary residuals has been studied in many fields, and well established. However, the stationary assumption on the residuals seems to be restrictive. Therefore, we extend the model to the case when the residuals are locally stationary. The best linear unbiased estimator (BLUE) of coefficient vector contains the residual covariance matrix which is usually unknown. Hence we often use the least squares estimator (LSE) which is always feasible, but is not efficient generally. We evaluate the asymptotic covariance matrices of BLUE and LSE. We also study the efficiency of the LSE relative to the BLUE.