Tail-Heaviness, Asymmetry, and Profitability Forecasting by Quantile Regression

Abstract

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.

Robust approach to earnings forecast: A comparison

“…We integrate the forecasting approaches of Ohlson and Kim (2015), Tian et al (2021), and Qu (2021). The six models examined in this paper have different explanatory variables.…”

“…Ohlson and Kim (2015) evaluate the relative efficiency of OLS versus TS in several cross‐sectional valuation settings, including Models 4 and 5. Finally, Tian et al (2021) contrast the relative forecasting accuracy of OLS and QR using Model 6. In each case, the proposed robust estimation method outperforms the OLS method.…”

“…The model parameter μ j,t and v j,T are indexed by industry j and T to highlight that the estimation is done on an industry‐specific basis and for each year T using the previous 5 years of data. Tian et al (2021) classify industries based on the first‐digit standard industry classification (SIC). We classify industries based on the industry code formulated by Shenzhen and Shanghai Stock Exchange in this paper because the data are from Chinese financial market.…”

“…In Model 6, we apply similar filters in Tian et al (2021) to the sample data. Firstly, when analyzing a specific profitability measure, we exclude observations with the profitability measure exceeding one in absolute value.…”

“…The conclusion remains valid even if one winsorizes and scales the variables. Tian et al (2021) show that the quantile regression (QR) outperforms the OLS regression in profitability forecasting for various criteria including the mean absolute forecast error (MAFE). Qu (2021) documents the MM estimation improves the earnings forecast of the post‐winsorization OLS estimation, especially for those earning models with multiple explanatory variables.…”