论文标题
L2 - 释放：随着预测组合和投资组合分析的应用
L2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis
论文作者
论文摘要
本文解决了许多预测或许多资产的最小差异组合选择的预测组合。提出了一个称为L2 - 释放的新型凸问题。与标准配方相反，L2 - 释放最小化重量矢量的平方欧几里得规范受到一组松弛的线性不等式约束。由调谐参数控制的松弛程度平衡偏差和方差。当各个预测错误或金融资产的方差 - 可达（VC）矩阵表现出潜在的组结构 - 块等效矩阵加上用于特质的VC时，L2-弹性的解决方案可提供大致相等的组内权重。当渐近框架框架的数量$ n $的增长速度比时间尺寸$ t $快得多，新方法的最优性是在渐近框架下建立的。在蒙特卡洛模拟中证明了我们方法的出色有限样本性能。在三个有关微观经济学，宏观经济学和金融经验应用的实际数据示例中，强调了其广泛的适用性。
This paper tackles forecast combination with many forecasts or minimum variance portfolio selection with many assets. A novel convex problem called L2-relaxation is proposed. In contrast to standard formulations, L2-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequality constraints. The magnitude of relaxation, controlled by a tuning parameter, balances the bias and variance. When the variance-covariance (VC) matrix of the individual forecast errors or financial assets exhibits latent group structures -- a block equicorrelation matrix plus a VC for idiosyncratic noises, the solution to L2-relaxation delivers roughly equal within-group weights. Optimality of the new method is established under the asymptotic framework when the number of the cross-sectional units $N$ potentially grows much faster than the time dimension $T$. Excellent finite sample performance of our method is demonstrated in Monte Carlo simulations. Its wide applicability is highlighted in three real data examples concerning empirical applications of microeconomics, macroeconomics, and finance.
