TEST FOR ZERO MEDIAN OF ERRORS IN AN ARMA-GARCH MODEL
TEST FOR ZERO MEDIAN OF ERRORS IN AN ARMA-GARCH MODEL
复制标题
ARMA-GARCH 模型的零均值和零中位数测试
DOI：
10.1017/s0266466621000244
复制
发表时间：
2021-06-09
影响因子：
0.8
通讯作者：
Zhang, Rongmao
中科院分区：
文献类型：
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作者：
Ma, Yaolan;Zhou, Mo;Zhang, Rongmao
由于ARMA-GARCH模型所生成的数据具有偏度、重尾、波动性持续性等重要特性，已成为分析金融经济数据的基准模型。常用的拟极大似然估计（QMLE）要求误差和序列本身都有有限的第四矩，以确保正常极限。自加权拟最大指数似然估计（SWQMELE）通过假设误差及其绝对值的中位数为零和平均值分别为一，减少了矩约束。因此，在应用SWQMELE之前，有必要对误差中值为零进行检验，因为将零均值变为零中值会破坏ARMA-GARCH结构。本文提出了一种不需要估计GARCH模型，而是利用GARCH结构来减小矩效应的有效的经验似然检验方法。仿真研究证实了该方法的有效性。数据分析表明，一些财务回报的误差中位数不为零，这对SWQMELE的使用提出了警告。
Because the ARMA-GARCH model can generate data with some important properties such as skewness, heavy tails, and volatility persistence, it has become a benchmark model in analyzing financial and economic data. The commonly employed quasi maximum likelihood estimation (QMLE) requires a finite fourth moment for both errors and the sequence itself to ensure a normal limit. The self-weighted quasi maximum exponential likelihood estimation (SWQMELE) reduces the moment constraints by assuming that the errors and their absolute values have median zero and mean one, respectively. Therefore, it is necessary to test zero median of errors before applying the SWQMELE, as changing zero mean to zero median destroys the ARMA-GARCH structure. This paper develops an efficient empirical likelihood test without estimating the GARCH model but using the GARCH structure to reduce the moment effect. A simulation study confirms the effectiveness of the proposed test. The data analysis shows that some financial returns do not have zero median of errors, which cautions the use of the SWQMELE.