LASSO introduces shrinkage bias into estimated coefficients, which can adversely affect the desirable asymptotic normality and invalidate the standard inferential procedure based on the $t$-statistic. The desparsified LASSO has emerged as a well-known remedy for this issue. In the context of high dimensional predictive regression, the desparsified LASSO faces an additional challenge: the Stambaugh bias arising from nonstationary regressors. To restore the standard inferential procedure, we propose a novel estimator called IVX-desparsified LASSO (XDlasso). XDlasso eliminates the shrinkage bias and the Stambaugh bias simultaneously and does not require prior knowledge about the identities of nonstationary and stationary regressors. We establish the asymptotic properties of XDlasso for hypothesis testing, and our theoretical findings are supported by Monte Carlo simulations. Applying our method to real-world applications from the FRED-MD database -- which includes a rich set of control variables -- we investigate two important empirical questions: (i) the predictability of the U.S. stock returns based on the earnings-price ratio, and (ii) the predictability of the U.S. inflation using the unemployment rate.

翻译：LASSO在估计系数中引入了收缩偏差，这可能对理想的渐近正态性产生不利影响，并使基于$t$统计量的标准推断程序失效。去稀疏化LASSO已成为解决此问题的知名方法。在高维预测回归背景下，去稀疏化LASSO面临一个额外挑战：由非平稳回归变量引起的Stambaugh偏差。为恢复标准推断程序，我们提出了一种名为IVX-去稀疏化LASSO（XDlasso）的新型估计量。XDlasso能同时消除收缩偏差和Stambaugh偏差，且无需预先获知非平稳与平稳回归变量的具体身份。我们建立了XDlasso用于假设检验的渐近性质，并通过蒙特卡洛模拟验证了理论结果。将我们的方法应用于FRED-MD数据库的实际案例（该数据库包含丰富的控制变量集），我们研究了两个重要的实证问题：（i）基于收益价格比预测美国股票收益的可预测性；（ii）利用失业率预测美国通胀的可预测性。