A comparative study of monotone quantile regression methods for financial returns - Yuzhi Cai (International Journal of Theoretical and Applied Finance, 2016)
Quantile regression methods have been used widely in finance to alleviate estimationproblems related to the impact of outliers and the fat-tailed error distribution of financialreturns. However, a potential problem with the conventional quantile regression methodis that the estimated conditional quantiles may cross over, leading to a failure of theanalysis. It is noticed that the crossing over issues usually occur at high or low quantilelevels, which are the quantile levels of great interest when analyzing financial returns.Several methods have appeared in the literature to tackle this problem. This studycompares three methods, i.e. Cai & Jiang, Bondell et al. and Schnabel & Eilers, forestimating noncrossing conditional quantiles by using four financial return series. Wefound that all these methods provide similar quantiles at nonextreme quantile levels.However, at extreme quantile levels, the methods of Bondell et al. and Schnabel & Eilersmay underestimate (overestimate) upper (lower) extreme quantiles, while that of Cai &Jiang may overestimate (underestimate) upper (lower) extreme quantiles. All methodsprovide similar median forecasts.