This study proposes a novel method for forecasting a scalar variable based on high-dimensional predictors that is applicable to various data distributions. In the literature, one of the popular approaches for forecasting with many predictors is to use factor models. However, these traditional methods are ineffective when the data exhibit non-Gaussian characteristics such as skewness or heavy tails. In this study, we newly utilize a quantile factor model to extract quantile factors that describe specific quantiles of the data beyond the mean factor. We then build a quantile-based forecast model using the estimated quantile factors at different quantile levels as predictors. Finally, the predicted values at the various quantile levels are combined into a single forecast as a weighted average with weights determined by a Markov chain based on past trends of the target variable. The main idea of the proposed method is to incorporate a quantile approach to a forecasting method to handle non-Gaussian characteristics effectively. The performance of the proposed method is evaluated through a simulation study and real data analysis of PM2.5 data in South Korea, where the proposed method outperforms other existing methods in most cases.

翻译：本研究提出了一种基于高维预测变量对标量变量进行预测的新方法，该方法适用于多种数据分布。在现有文献中，利用大量预测变量进行预测的常用方法之一是使用因子模型。然而，当数据呈现偏态或重尾等非高斯特征时，这些传统方法效果不佳。本研究创新性地采用分位数因子模型，提取描述数据特定分位数（而非仅均值因子）的分位数因子。随后，我们利用不同分位数水平下估计得到的分位数因子作为预测变量，构建基于分位数的预测模型。最后，将各分位数水平下的预测值通过加权平均方式合并为单一预测值，其权重由基于目标变量历史趋势的马尔可夫链确定。该方法的核心思想是将分位数方法融入预测框架，以有效处理非高斯特征。通过模拟研究及韩国PM2.5真实数据分析评估了所提方法的性能，结果表明在多数情况下该方法优于现有其他方法。