Factor modeling is a powerful statistical technique that permits common dynamics to be captured in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and widespread use for various applications ranging from genomics to finance, this methodology has predominantly remained linear. This study estimates factors nonlinearly through the kernel method, which allows for flexible nonlinearities while still avoiding the curse of dimensionality. We focus on factor-augmented forecasting of a single time series in a high-dimensional setting, known as diffusion index forecasting in macroeconomics literature. Our main contribution is twofold. First, we show that the proposed estimator is consistent and it nests the linear principal component analysis estimator as well as some nonlinear estimators introduced in the literature as specific examples. Second, our empirical application to a classical macroeconomic dataset demonstrates that this approach can offer substantial advantages over mainstream methods.

因子建模是一种强大的统计技术，它允许在具有一些潜在变量或因子的大型数据面板中捕获共同动态，从而减轻维度灾难。尽管它在从基因组学到金融的各种应用中广受欢迎并被广泛使用，但这种方法主要保持线性。本研究通过核方法非线性地估计因子，该方法允许灵活的非线性，同时仍避免维数灾难。我们专注于高维环境中单个时间序列的因子增强预测，在宏观经济学文献中称为扩散指数预测。我们的主要贡献是双重的。第一的，我们表明所提出的估计量是一致的，它嵌套了线性主成分分析估计量以及文献中作为具体例子引入的一些非线性估计量。其次，我们对经典宏观经济数据集的实证应用表明，这种方法可以提供比主流方法更大的优势。