A Quantile Regression Approach to Equity Premium Prediction

Abstract

We propose a quantile regression approach to equity premium forecasting. Robust point forecasts are generated from a set of quantile forecasts, using both …xed and time-varying weighting schemes, thus exploiting the entire distributional information associated with each predictor. Further gains are achieved by incorporating the forecast combination methodology in our quantile regression setting. Our approach using a time-varying weighting scheme delivers statistically and economically signi…cant out-of-sample forecasts relative to both the historical average benchmark and the combined predictive mean regression modeling approach.JEL classi…cation: G11; G12; C22; C53

Stock return distribution and predictability: Evidence from over a century of daily data on the DJIA index

“…Cenesizoglou and Timmermann (2008) report predictive power for economic variables for future stock returns, too, especially in the right tail but not in the distribution's center. The same result of predictive power which is heterogeneous over future quantiles is obtained by Meligkotsidou et al (2014), who also propose two approaches of forecasting future mean by combining individual variables' predictions-combining quantiles predicted by each variable first, and combining those predicted values across variables second, or combining predictions for each quantile separately (across all predictors) first, and combining predicted quantiles next, all with constant or time-varying endogenously optimised weights.…”

“…These predicted quantile returns (except for the median) are then employed to calculate the predicted mean return for each year in the prediction/OOS period. 13 In the next step, in the spirit of Rapach et al (2010) and Meligkotsidou et al (2014), we calculate the predicted mean at t+1 as an equally weighted sum of t+1 predicted quantile returns. 14 Two approaches are adopted here.…”

“…It does have predictive power for other quantiles of future return distribution, however. 14 This is the simplest weighting scheme possible and more advanced techniques could be used, potentially to obtain forecasts that are more accurate; however, the literature demonstrated that a simple average often outperforms those more advanced approaches (seeMeligkotsidou et al, 2014, or Timmermann (2006 andAiolfi et al (2011) who provide reviews of theoretical arguments and empirical evidence in support of simple forecast aggregation methods). However, our aim is to show that even such a naïve scheme can generate superior forecasts.…”

Quantile forecast combinations in realised volatility prediction

“…While the QAR methodology described so far provides a direct way for forecasting the quantiles of interest along with an approximate forecast distribution, forecasting the mean of future realised volatility is not trivial. For a given model specification or a given complete subset that has been used for producing quantile forecasts, point forecasts can be constructed as weighted averages of a set of quantile forecasts (Meligkotsidou et al 2014a). The weights represent probabilities attached to different quantile forecasts, suggesting how likely to predict the return at the next period each regression quantile is.…”

“…The most important finding that emerges is that the augmented QAR models are more accurate than the AR(q) benchmark. In more detail, forecast accuracy, judged by the statistical significance of the QS tests, is more pronounced for the left tail (τ = 0.10, τ = 0 25). and the central to right tail part (τ = 2/3, τ = 0.75) of the realised volatility distribution.…”