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针对金融资产收益率分布呈现的尖峰、厚尾及有偏的特点,沿袭变换核密度估计的思想,提出一种广义Logistic变换,对变换后的样本应用Beta核密度估计以消除边界偏差,模拟试验表明,该方法显著提高了对尖峰厚尾分布密度的估计精度.继而将该方法与参数化的GARCH设定相结合,建立一种半参数GARCH模型.该模型具有两个优点:第一,基于变换核密度估计可更加准确地估计收益率的条件分布;第二,通过迭代提高了参数估计的稳健性.模拟试验表明,较之伪极大似然估计法和基于离散最大惩罚似然估计的半参数方法,该方法大大提高了参数估计的相对效率.对沪深300指数的实证研究验证了本文模型的有效性.
Aiming at the spikes, thick tails and biased features of the return distribution of financial assets, a generalized Logistic transformation is proposed along with the idea of transformed kernel density estimation. Beta kernel density estimation is applied to the transformed samples to eliminate the boundary deviation. The simulation experiment It is shown that this method significantly improves the accuracy of the estimation of the distribution density of peak and thick tail.Then this method is combined with the parameterized GARCH setting to establish a semiparametric GARCH model.This model has two advantages: Transforming the kernel density estimation can estimate the conditional distribution of the yield more accurately. Second, the robustness of the parameter estimation is improved by iteration. Simulation results show that compared with the pseudo-maximum likelihood estimation method and the discrete maximum penalty likelihood estimation Semi-parametric method, which greatly improves the relative efficiency of parameter estimation.The empirical study of CSI300 Index validates the effectiveness of the proposed model.