Diffusion Indexes With Sparse Loadings

The use of large-dimensional factor models in forecasting has received much attention in the literature with the consensus being that improvements on forecasts can be achieved when comparing with standard models. However, recent contributions in the literature have demonstrated that care needs to be taken when choosing which variables to include in the model. A number of different approaches to determining these variables have been put forward. These are, however, often based on ad hoc procedures or abandon the underlying theoretical factor model. In this article, we will take a different approach to the problem by using the least absolute shrinkage and selection operator (LASSO) as a variable selection method to choose between the possible variables and thus obtain sparse loadings from which factors or diffusion indexes can be formed. This allows us to build a more parsimonious factor model that is better suited for forecasting compared to the traditional principal components (PC) approach. We provide an asymptotic analysis of the estimator and illustrate its merits empirically in a forecasting experiment based on U.S. macroeconomic data. Overall we find that compared to PC we obtain improvements in forecasting accuracy and thus find it to be an important alternative to PC. Supplementary materials for this article are available online.高维因子模型（large-dimensional factor models）在预测领域的应用已受到学术研究的广泛关注，学界普遍认为，相较于标准模型，该类模型可提升预测精度。然而，近期的学术研究表明，在选取模型纳入的变量时需格外谨慎。目前已提出多种用于确定这些变量的方法，但此类方法往往基于特设程序，或是摒弃了其底层的理论因子模型框架。本文采用一种全新的思路解决该问题：以最小绝对收缩和选择算子（least absolute shrinkage and selection operator, LASSO）作为变量选择方法，从候选变量中筛选出有效变量，进而得到稀疏载荷，据此可构建因子或扩散指数。这使得我们能够构建比传统主成分（principal components, PC）方法更为简约的因子模型，更适配预测任务。本文对该估计量进行了渐近分析，并基于美国宏观经济数据开展预测实验，实证验证了该方法的优势。整体而言，相较于传统主成分方法，本文提出的方法可提升预测精度，是主成分方法的重要替代方案。本文补充材料可在线获取。