Ӧ�ø���ͳ�� 2010, 26(5) 485-500 DOI:      ISSN: 1001-4268 CN: 31-1256

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������ʧ(Expected Shortfall, ES)�ǵ���
�����еĽ����ʲ����չ���Ĺ���֮һ, ��һ�������һ���Է��ն���.
������$\alpha$-������о�����˥�����ϵ��������,
�������˹��ƹ�����ն���ES��ֵ, ��һ�������ռ�ֵ(Value at Risk,
VaR)�ĺ˹���, �ڶ�����ES�ĺ˹���. �õ�ES�ĺ˹�������\, Bahadur��ʾ,
�Լ��������ͽ�����̬�Ե������ٶ�.

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Two-Step Kernel Estimation of Expected Shortfall for
Strong Mixing Time Series
Liu Jing,Yang Shanchao,Yao Yongyuan
Guangxi Normal University
Abstract:

Expected Shortfall (ES) is one of the most
popular tools of risk management for financial property, and is an
ideal coherent risk measure. In this paper, we discuss the two-step
kernel estimator of ES under polynomial decay of strong mixing
coefficients of time series. The first step is the kernel estimator
of VaR (Value at Risk) and the second step is the kernel estimator
of ES. We obtain Bahadur representation of the kernel estimator of
ES. Then, we give the mean squares error and the rate of the
asymptotic normality.

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