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Focusing on a high dimensional linear model $y = X\beta + \epsilon$ withdependent, non-stationary, and heteroskedastic errors, this paper applies thedebiased and threshold ridge regression method that gives a consistentestimator for linear combinations of $\beta$; and derives a Gaussianapproximation theorem for the estimator. Besides, it proposes a dependent wildbootstrap algorithm to construct the estimator's confidence intervals andperform hypothesis testing. Numerical experiments on the proposed estimator andthe bootstrap algorithm show that they have favorable finite sampleperformance.  Research on a high dimensional linear model with dependent(non-stationary)errors is sparse, and our work should bring some new insights to this field.

Debiased and threshold ridge regression for linear model with heteroskedastic and dependent error