统计研究 ›› 2018, Vol. 35 ›› Issue (11): 116-128.doi: 10.19343/j.cnki.11-1302/c.2018.11.010

• • 上一篇    

基于回归的时变偏度和时变峰度识别检验

贾婧等   

  • 出版日期:2018-11-25 发布日期:2018-11-23

Regression-based Testsfor Identifying Time-varying Skewness and Kurtosis

Jia Jing et al   

  • Online:2018-11-25 Published:2018-11-23

摘要: 资产收益率时变高阶矩建模的首要前提是资产收益率的偏度和峰度具有时变性,即资产收益率存在类似于异方差性的异偏度和异峰度特征。目前文献中的时变偏度和时变峰度识别检验存在适用性较差且检验功效较低等不足。本文提出基于回归的检验方法识别资产收益率偏度和峰度的时变性。该检验一方面利用概率积分变换缓解了拉格朗日乘数检验对资产收益率序列的高阶矩存在性的限制,另一方面考虑了检验统计量中参数估计的不确定性对其统计性质的影响,具有良好的渐近统计性质且适用性更广。蒙特卡洛模拟表明该检验具有良好的有限样本性质,具有合适的检验水平和较高的检验功效。最后,将基于回归的检验运用于上证综指和深圳成指收益率的时变建模研究中。

关键词: 时变高阶矩, 基于回归的检验, 拉格朗日乘数检验, 游程检验

Abstract: The first prerequisite for establishing the time-varying higher order moment model is that the skewness and kurtosis of asset returns have the time-varying characteristics, namely, there exist characters of hetero-skewness or hetero-kurtosis in the assets returns rates similar to heteroscedasticity. In the present literature, there is a poor application and low efficiency in identifying and testing the time-varying skewness and time-varying kurtosis. This paper proposes a regression-based test to identifytime-varying skewness and kurtosis for assets returns rate. On one hand, it uses the probability integral transformation to reduce the constraints on the existence of the higher order moments of the assets returns series by the Lagrange Multiplier Test.On the other hand, it takes the impact of the parameter estimation uncertainty on the statistical properties of this test into consideration, making it with better asymptotic statistical properties and widely applicable. The Monte Carlo simulation further indicates that the regression-based test has a good finite sample property with a suitable empirical size and a high empirical power. Finally, this regression-based testis applied to the time-varying properties of the returns series forShanghai and ShenzhenComposite Indexes.

Key words: Time-varying Higher Order Moments, Regression-based Test, Lagrange Multiplier Test, Runs Test