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 paper we will take a different approach to the problem by using the 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 which 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 US 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.

高维因子模型在预测领域的应用已受到学界广泛关注，现有研究共识表明，相较于标准模型，此类模型可提升预测效果。然而，近期文献成果显示，在选择模型纳入的变量时需格外谨慎。目前已有多种不同方法用于确定这些变量，但这些方法往往基于特设流程，或是摒弃了底层的理论因子模型。本文采用不同的研究思路：将套索回归（LASSO）作为变量选择方法，从候选变量中筛选出合适的变量，进而得到可用于构建因子或扩散指数的稀疏载荷。由此我们可构建比传统主成分（PC）方法更具简约性的因子模型，更适配预测任务。我们对该估计量开展了渐近分析，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。总体而言，相较于主成分方法，本方法可提升预测精度，因此是主成分方法的重要替代方案。