L_p quantile regression with realized measure

A new financial risk model named L_p quantile regression with a realized measure (realized L_p quantile) was proposed. The realized measure and L_p quantiles were combined and L_p quantile were added to the measurement equation. The realized Lp quantile model is a generic model that includes realized quantile model and expectile model. An asymmetric exponential power distribution (AExpPow) was proposed to derive the formula of log-likelihood. And a simulation was conducted to justify the validity of the log-likelihood. Finally an empirical study was conducted to justify the validity of the realized L_p quantile. And some conclusions were drawn as follows: differfent power indices suit different data and different time-frequencies suit different realized measures, and higher frequency is not always better.