非线性因子模型的核技巧
The Kernel Trick for Nonlinear Factor Modeling
摘要：
因子建模是一种功能强大的统计技术，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的动态，从而减轻维度灾难。尽管这种方法很受欢迎，并广泛用于从基因组学到金融的各种应用，但它主要是线性的。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，同时仍然避免维数灾难。我们专注于一个单一的时间序列在一个高维的设置，被称为扩散指数预测在宏观经济学文献的因子增强预测。我们的主要贡献是双重的。首先，我们证明了所提出的估计是一致的，它嵌套的线性PCA估计，以及在文献中介绍的一些非线性估计作为具体的例子。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。
英文摘要：
Factor modeling is a powerful statistical technique that permits to capture the common dynamics 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 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 linear PCA 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
