Inference for high-dimensional linear models with locally stationary error processes

Linear regression models with stationary errors are well studied but the non-stationary assumption is more realistic in practice. An estimation and inference procedure for high-dimensional linear regression models with locally stationary error processes is developed. Combined with a proper estimator for the autocovariance matrix of the non-stationary error, the desparsified lasso estimator is adopted for the statistical inference of the regression coefficients under the fixed design setting. The consistency and asymptotic normality of the desparsified estimators is established under certain regularity conditions. Element-wise confidence intervals for regression coefficients are constructed. The finite sample performance of our method is assessed by simulation and real data analysis.