Tail-Heaviness, Asymmetry, and Profitability Forecasting by Quantile Regression
研究发现分位数回归在预测盈利时优于普通最小二乘法，且盈利分布尾部越厚重，分位数回归的预测越准确；不对称性对预测精度呈U形或倒U形影响。
We show that quantile regression is better than ordinary-least-squares (OLS) regression in forecasting profitability for a range of profitability measures following the conventional setup of the accounting literature, including the mean absolute forecast error (MAFE) evaluation criterion. Moreover, we perform both a simulated-data and an archival-data analysis to examine how the forecasting performance of quantile regression against OLS changes with the shape of the profitability distribution. Considering the MAFE and mean squared forecast error (MSFE) criteria together, we see that the quantile regression is more accurate relative to OLS when the profitability to be forecast has a heavier-tailed distribution. In addition, the asymmetry of the profitability distribution has either a U-shape or an inverted-U-shape effect on the forecasting accuracy of quantile regression. An application of the distributional shape analysis framework to cash flow forecasting demonstrates the usefulness of the framework beyond profitability forecasting, providing additional empirical evidence on the positive effect of tail-heaviness and supporting the notion of an inverted-U-shape effect of asymmetry. This paper was accepted by Shiva Rajgopal, accounting.