基于高频数据的GARCH模型拟极大指数似然估计的一种portmanteau Q检验

A portmanteau test for quasi maximum exponential likehood estimation of GARCH model based on high frequency data

已有研究表明,基于高频数据的GARCH模型的拟极大指数似然估计可以提升估计精度,但鲜有研究就该估计量的性质推导其对应的检验统计量。文章基于高频数据的GARCH拟极大指数似然估计性质,提出一种portmanteau Q检验统计量,通过模拟验证了该检验统计量的理论正确性,并选取沪深300、中证500和上证50等3个指数进行了具体应用。结果显示,在模型充分时,文章提出的检验统计量的分布更近似理论推导的分布,优于基于低频数据的检验统计量结果,且由于包含高频信息,该统计量能更好地捕捉高频残差自相关性;而当低频残差自相关性时,即使相关性较弱,该统计量也能识别模型是否充分,对GARCH模型的阶数识别有一定效果。实证研究也表明,该检验统计量能对高频信息有效利用,具有一定的实用性。

Previous studies have shown that the quasi maximum exponential likelihood estimation based on high frequency data can improve the estimation accuracy of GARCH model,but few studies have derived the corresponding test statistic for this estimator.In this paper,a portmanteau Q test sta-tistic is proposed based on the asymptotic property of quasi maximum exponential likelihood estimation of GARCH model based on high-frequency data.The theoretical correctness of the test statistic is vali-dated through simulation in this paper,and specific applications are provided by using the data of the CSI 300,CSI 500,and SSE 50 indices.The results show that when the model is adequate,the distri-bution of the test statistic proposed in this paper more closely follows the theoretically derived distribu-tion,which is better than the results of the test statistic based on low-frequency data.Moreover,the statistic is able to capture high-frequency residual autocorrelation due to the inclusion of high-frequen-cy information.While for low-frequency residual autocorrelation,the statistic can also identify model non-sufficiency when the correlation is stronger,which is useful for order identification in GARCH model.Empirical research also indicates that the test statistic can identify the effective utilization of high-frequency information by the models based on high-frequency data,demonstrating a certain de-gree of practicality.