Biweighted Composite Regression Estimation Of GARCH Models

Firstly,this paper outlines the GARCH model and its parameter estimation,and then introduces the research progress of Quantile Regression(QR)estimation.Finally,elaborates the process and properties of parameter estimation improvement,digs out research gaps and innovations from the essence of evolution in estimation,and puts forward a new estimation.And prove its theoretical large sample properties.This paper dedicated to the study of parameter estimation in GARCH model.Maximum Likelihood Estimation(MLE)has the limitations of parameter assumptions.Therefore,estimations such as Quasi-Maximum Likelihood Estimation(QMLE)and Least Absolute Deviation(LAD)are derived.With the superior properties of the QR Theory,which is widely used in parameter estimation of econometric models.Based on the goodness of Composite Quantile Regression(CQR),we consider the GARCH process and propose a more robust and efficacious estimator – Biweighted Composite Quantile Regression(BWCQR).Simulations are conducted to compare the performance of different estimators,and it demonstrates that the proposed BWCQR estimator is significantly outperforms than the traditional method of parameter estimations,such as QMLE,QR estimation and CQR estimation when the innovation follows a heavy-tailed distribution.At the same time,this paper verifies that it’s reasonable and feasible to apply the Bootstrap technology to make statistical inferences.For the sake of verification that the BWCQR is competent in the empirical studies,this paper also applies the BWCQR approach to three stocks.As an application,it’s selects three major stock market indexes data from 2015 to 2021 and uses the forward one-step prediction method to analyze and model the SCI,HSI and S&P 500 respectively.Empirical study shows that BWCQR can better establish the volatility system of three stock data than traditional method of estimations under the statistical evaluations and testings,which endorse our theoretical results.