Sufficient Forecasting for Sub-Gaussian Processes Using Factor Models

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.