Recent progress in forecasting emphasizes the role of nonlinear factor models. In the simplest case, the nonlinearity appears in the link function. But even in this case, the classical forecasting methods, such as principal components analysis, do not perform well. Another challenge when dealing specially with financial data is the heavy-tailedness of data. This brings another difficulty to the classical forecasting methods. There are recent works in sufficient forecasting which use the technique of sliced inverse regression and local regression methods to overcome the nonlinearity. In this paper, we first observe that for heavy-tailed data, the existing approaches fail. Then we show that a suitable combination of two known methods of kernel principal component analysis and k-nearest neighbor regression improves the forecasting dramatically.

中文翻译：

---

使用因子模型对亚高斯过程进行充分预测

预测的最新进展强调了非线性因子模型的作用。在最简单的情况下，非线性出现在链接函数中。但即使在这种情况下，经典的预测方法，如主成分分析，也表现不佳。专门处理财务数据时的另一个挑战是数据的重尾性。这给经典的预测方法带来了另一个困难。最近的充分预测工作使用切片逆回归技术和局部回归方法来克服非线性。在本文中，我们首先观察到对于重尾数据，现有方法会失败。然后我们展示了两种已知的核主成分分析方法的适当组合和ķ-最近邻回归显着改善了预测。