论文标题
高维预测回归的拉索
On LASSO for High Dimensional Predictive Regression
论文作者
论文摘要
本文研究了在高维线性预测回归中，Lasso是一种广泛使用的$ L_ {1} $ - 惩罚回归方法，尤其是当潜在预测变量的数量超过样本量并且存在许多单位根回归器时。拉索的一致性取决于两个关键组成部分：回归器的跨产物和误差项的偏差结合，以及革兰氏矩阵的受限特征值。我们为这些组件提供了新的概率界限，这表明拉索的收敛速率与横截面病例中通常观察到的收敛速度不同。当应用于固定，非平稳和协整预测因子的混合物时，如果预测因子是标准标准的，则Lasso保持其渐近保证。 Lasso利用机器学习和宏观经济领域的专业知识，在预测失业率方面表现出了强劲的表现，这证明了其在FRED-MD数据库中的应用。
This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors are present. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix. We present new probabilistic bounds for these components, suggesting that LASSO's rates of convergence are different from those typically observed in cross-sectional cases. When applied to a mixture of stationary, nonstationary, and cointegrated predictors, LASSO maintains its asymptotic guarantee if predictors are scale-standardized. Leveraging machine learning and macroeconomic domain expertise, LASSO demonstrates strong performance in forecasting the unemployment rate, as evidenced by its application to the FRED-MD database.
