利用 Graphical LASSO 在结构突变下组合预测
Combining Forecasts under Structural Breaks Using Graphical LASSO
AI总结：
本文提出基于 Graphical LASSO 的预测组合方法，通过 FGL 分离共同与特质误差，并用 RD-FGL 与 ADMM 处理结构突变下的时变区制权重。
摘要：
本文开发了一种组合大量预测的新方法，该方法基于名为 Graphical LASSO（GL）的机器学习算法。我们将不同预测者的预测误差可视化为一个由相互作用实体构成的网络，并在存在共同因子结构和结构突变的情况下推广网络推断。首先，我们注意到预测者经常使用共同信息，因此会犯共同错误，这使预测误差呈现出共同因子结构。我们使用 Factor Graphical LASSO（FGL，Lee and Seregina (2023)）将共同预测误差与特质误差分离，并利用后者精度矩阵的稀疏性。其次，由于专家网络会随着时间推移而变化，以应对衰退等不稳定环境，假定预测组合权重恒定是不合理的。因此，我们提出 Regime-Dependent Factor Graphical LASSO（RD-FGL），它允许因子载荷和特质精度矩阵依赖于区制。我们使用 Alternating Direction Method of Multipliers（ADMM）开发了其可扩展实现，以估计依赖于区制的预测组合权重。利用欧洲央行专业预测者调查（ECB SPF）数据预测宏观经济序列的实证应用表明，使用 FGL 和 RD-FGL 的组合预测具有优越性能。
英文摘要：
In this paper we develop a novel method of combining many forecasts based on a machine learning algorithm called Graphical LASSO (GL). We visualize forecast errors from different forecasters as a network of interacting entities and generalize network inference in the presence of common factor structure and structural breaks. First, we note that forecasters often use common information and hence make common mistakes, which makes the forecast errors exhibit common factor structures. We use the Factor Graphical LASSO (FGL, Lee and Seregina (2023)) to separate common forecast errors from the idiosyncratic errors and exploit sparsity of the precision matrix of the latter. Second, since the network of experts changes over time as a response to unstable environments such as recessions, it is unreasonable to assume constant forecast combination weights. Hence, we propose Regime-Dependent Factor Graphical LASSO (RD-FGL) that allows factor loadings and idiosyncratic precision matrix to be regime-dependent. We develop its scalable implementation using the Alternating Direction Method of Multipliers (ADMM) to estimate regime-dependent forecast combination weights. The empirical application to forecasting macroeconomic series using the data of the European Central Bank's Survey of Professional Forecasters (ECB SPF) demonstrates superior performance of a combined forecast using FGL and RD-FGL.
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