The threshold GARCH(TGARCH)models have been very useful for analyzing asymmetric volatilities arising from financial time series.Most research on TGARCH has been directed to the stationary case.This paper studies the ...The threshold GARCH(TGARCH)models have been very useful for analyzing asymmetric volatilities arising from financial time series.Most research on TGARCH has been directed to the stationary case.This paper studies the estimation of non-stationary first order TGARCH models.Restricted normal mixture quasi-maximum likelihood estimation(NM-QMLE)for non-stationary TGARCH models is proposed in the sense that we estimate the other parameters with any fixed location parameter.We show that the proposed estimators(except location parameter)are consistent and asymptotically normal under mild regular conditions.The impact of relative leptokursis and skewness of the innovations’distribution and quasi-likelihood distributions on the asymptotic efficiency has been discussed.Numerical results lend further support to our theoretical results.Finally,an illustrated real example is presented.展开更多
The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estim...The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estimator,and called modified Pickands’estimator.The similar results about Hill’s estimator are also obtained,which generalize the corresponding results in.Besides,some comparisons between Hill’s estimator and the modified Pickands’estimator are given.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11101448)the Program for New Century Excellent Talents in University+3 种基金the Program for Young Talents of Beijing (Grant No.YETP0955)the Program for National Statistics Science Research Plan (Grant No.2013LY015)the "Project 211" of the Central University of Finance and Economicsthe Central University of Finance Young Scholar Innovation Fund
文摘The threshold GARCH(TGARCH)models have been very useful for analyzing asymmetric volatilities arising from financial time series.Most research on TGARCH has been directed to the stationary case.This paper studies the estimation of non-stationary first order TGARCH models.Restricted normal mixture quasi-maximum likelihood estimation(NM-QMLE)for non-stationary TGARCH models is proposed in the sense that we estimate the other parameters with any fixed location parameter.We show that the proposed estimators(except location parameter)are consistent and asymptotically normal under mild regular conditions.The impact of relative leptokursis and skewness of the innovations’distribution and quasi-likelihood distributions on the asymptotic efficiency has been discussed.Numerical results lend further support to our theoretical results.Finally,an illustrated real example is presented.
文摘The author obtains the rate of strong convergence,mean squared error and optimal choice of the“smoothing parameter”(the sample fraction)of a tail index estimator which was proposed by the author from Pickands’estimator,and called modified Pickands’estimator.The similar results about Hill’s estimator are also obtained,which generalize the corresponding results in.Besides,some comparisons between Hill’s estimator and the modified Pickands’estimator are given.
