Fitting an ARMA‐GARCH model has become a common practice in financial econometrics. Because the asymptotic normality of the quasi maximum likelihood estimation (QMLE) requires finite fourth moment for both errors and the sequence itself, self‐weighted quasi maximum exponential likelihood estimation (SWQMELE) has been proposed to reduce the moment constraints but requires the errors to have zero median instead of zero mean. Because changing zero mean to zero median destroys the ARMA‐GARCH structure and has a serious effect on skewed data, this paper proposes an efficient empirical likelihood test for zero mean of errors in the application of SWQMELE to ensure that the model still concerns conditional mean. A simulation study confirms the good finite sample performance before applying the test to the US housing price indexes and financial returns for the study of comovement.

中文翻译：

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SWQMELE在拟合ARMA-GARCH模型中应用的经验似然检验

拟合 ARMA-GARCH 模型已成为金融计量经济学中的常见做法。由于准最大似然估计 (QMLE) 的渐近正态性需要误差和序列本身的有限四阶矩，因此提出了自加权准最大指数似然估计 (SWQMELE) 以减少矩约束，但要求误差具有零中位数而不是零均值。由于将零均值改为零中值会破坏 ARMA-GARCH 结构并对偏斜数据产生严重影响，因此本文在 SWQMELE 应用中提出了一种有效的零均值经验似然检验，以确保模型仍然关注条件均值。