Parameter MEM Based On Robust Estimation And Its Application In Futures Market

For high-frequency financial data,many experts and scholars have proposed a series of models to study.These models are all used to study the single non-negative financial high-frequency time series and there is little difference in theory.In order to study these non-negative financial high-frequency time series in a unified way,Engle(2002)proposed a generalized model: Multiplicative Error Model(MEM).At present,the most widely used parameter estimation method for MEM is Maximum Likelihood Estimation(MLE).However,the high-frequency data in real financial market often have heavy tails and contain many outliers,and the variance of these data may even be infinite,which makes it unreasonable for MLE to assume that the error variance is limited directly in the estimation of high-frequency data in real financial market,and once the error distribution assumed in advance is not real.The result will be unreliable.In order to solve the problem of MLE,this paper adopts the robust estimation method:firstly,MEM is estimated by M-estimation,but M-estimation gives the same weight to outliers and normal points,which is slightly unreasonable;secondly,considering the self-weighted M-estimation(SM-estimation),SM-estimation can give different weights to outliers according to the size of outliers,further reducing the impact of outliers on the estimation results.This paper also proves the consistency and asymptotic normality of SM-estimation in theory.At the same time,the numerical simulation is carried out when the error obeys Pareto distribution,Burr distribution and Fréchet distribution.Through simulation,it is found that the Bias and MSE of the robust estimation under parametric MEM(1,1)are generally smaller than MLE.Even after adding outliers to the data,the effect of MLE is not ideal,but the effect of the robust estimation is better.Finally,parametric MEM(1,1)under the robust estimation is applied to the two futures of polyethylene and polypropylene in Dalian Commodity Exchange.The price range,volume and turnover of the two futures in the same time period are modeled and compared.It is found that the Logarithmic Likelihood(LogL)ofthe parameter estimation results under the robust estimation is larger than that of MLE,and the Chichi Information Criterion(AIC)under the robust estimation is smaller than MLE,which indicates that the robust estimation is more suitable for parameter estimation of parametric MEM.