  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.
