Forecasting High-Dimensional Non-Normal Time Series Using Averaged Quantile Regression

Abstract This paper proposes a forecasting method based on averaged quantile regression to improve predictions for non-normally distributed data. Traditional forecasting models often rely on ordinary least squares, assuming normally distributed errors, which can be restrictive in practice. By leveraging quantile regression, our approach provides a more robust alternative that captures the varying effects of predictors across different quantiles of the response variable. The key contribution of this study is to introduce averaged quantile regression (AQR) as a flexible and effective forecasting tool for high-dimensional, non-normally distributed time series. We show that AQR outperforms conventional mean-based forecasting in a factor modeling setting and remains robust across diverse heavy-tailed, skewed, and near-normal distributions. While our method can be applied broadly, we illustrate its effectiveness within the dynamic factor model framework through numerical experiments and real data analysis.