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，这可能对期望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。在高维预测回归的背景下，去稀疏化LASSO面临一个额外的挑战：由非平稳回归变量产生的Stambaugh偏差。为了恢复标准推断程序，我们提出了一种称为IVX-去稀疏化LASSO（XDlasso）的新型估计量。XDlasso能够同时消除收缩偏差和Stambaugh偏差，且无需事先了解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我们的理论发现。将我们的方法应用于FRED-MD数据库中的实际应用——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，以及（ii）使用失业率预测美国通胀的可预测性。