LASSO inflicts shrinkage bias on estimated coefficients, which undermines asymptotic normality and invalidates standard inferential procedures based on the t-statistic. Given cross sectional data, the desparsified LASSO has emerged as a well-known remedy for correcting the shrinkage bias. In the context of high dimensional predictive regression, the desparsified LASSO faces an additional challenge: the Stambaugh bias arising from nonstationary regressors modeled as local unit roots. To restore standard inference, we propose a novel estimator called IVX-desparsified LASSO (XDlasso). XDlasso simultaneously eliminates both shrinkage bias and Stambaugh bias 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, 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.

翻译：LASSO对估计系数施加了收缩偏差，这破坏了渐近正态性，并使基于t统计量的标准推断程序失效。给定横截面数据，去稀疏化LASSO已成为纠正收缩偏差的常用方法。在高维预测回归的背景下，去稀疏化LASSO面临一个额外挑战：由局部单位根建模的非平稳回归变量产生的Stambaugh偏差。为恢复标准推断，我们提出一种名为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，且无需预先知晓非平稳与平稳回归变量的身份信息。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。将本方法应用于FRED-MD数据库的实际案例，我们研究了两个重要实证问题：（i）基于市盈率的美国股票收益率可预测性；（ii）利用失业率预测美国通货膨胀的可预测性。