基于变换核密度估计的半参数GARCH模型

Semi-parametric GARCH model based on transformed kernel density estimation

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.

In allusion to the leptokurtosis, fat-tail and skewness of the distribution of financial returns, thispaper follows the transformed kernel density estimation, proposing a generalized logistic transformation,and beta kernel estimation is then employed for the transformed data in order to eliminate boundary bias.Simulation experiments show that the proposed method considerably improves the accuracy of the densityestimation for peaked and fat-tailed distributions. A semi-parametric GARCH model is constructed bycombining the approach with parametric GARCH settings. This semi-parametric model has two advan-tages first, it can estimate the conditional density more accurately based on the proposed transformedkernel density estiination; second, it improves the robustness of estimation through iterations. Simulationstudies show that, compared with quasi maximum likelihood estimation and the semi-parametric methodbased on discrete maximum penalized likelihood estimation, the method proposed is more efficient. Em-pirical research with CSI 300 index verifies the validity of the model.