Composite Quanti Le Estimation For Sample A-PARCH Model And Its Applications In Volatility

Financial risk is an intrinsic property that cannot be eliminated in financial activities,while volatility is one of the most commonly used risk measures.Due to some characteristics of the volatility,we always use ARCH model and the GARCH model to fit it.Although these two types of models can construct an unconditional distribution of peaks and thick tails,they cannot describe the leverage effect of impact.In view of this,this paper uses the A-PARCH model to characterize the volatility of the rate of return.Maximum likelihood estimation and quantile regression estimation used more frequently in the model literature on volatility above.The maximum likelihood estimation,however,is susceptible to anomalous points,and the error distribution needs to be assumed beforehand.While the quantile regression estimation susceptible to the quantile position.In this paper,we firstly use CQR to estimate the A-PARCH(1,0)model and proved the asymptotic normality of the estimator under certain assumptions.Then we conducted a numerical simulation,compared with the quantile regression(QR)with abnormal values under three distributions,we can found that the estimation effect of CQR is better from the results of MAE and RMSE.In view of the excellent performance of CQR estimation in the thick-tailed data,we prefer CQR when modeling the A-PARCH(1,0)under the data of the Dow Jones Index,the Standard&Poor's 500 Index and the Shanghai Composite Index for the past 11 years.The estimation results of the CQR were compared with the results of quantile regression(QR)and the maximum likelihood estimation(MLE).The results show that the CQR estimation is better.RMSE has a significant decrease.Due to the excellent performance of CQR in numerical simulation and empirical analysis,the A-PARCH model based on CQR estimation can more effectively describe the aggregation effect and leverage effect of financial return rate.