Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models With StudenttInnovations
为条件分布为多元t分布的异方差动态回归模型，提供了得分、海森矩阵和信息矩阵的解析表达式，并推导了基于标准化新息平方范数的拉格朗日乘子检验，用于检验多元正态性vs多元t分布。蒙特卡洛模拟和英国26个行业股票收益的实证表明其条件分布具有厚尾特征。
We provide numerically reliable analytical expressions for the score, Hessian, and information matrix of conditionally heteroscedastic dynamic regression models when the conditional distribution is multivariatet. We also derive one-sided and two-sided Lagrange multiplier tests for multivariate normality versus multivariate t based on the first two moments of the squared norm of the standardized innovations evaluated at the Gaussian pseudo-maximum likelihood estimators of the conditional mean and variance parameters. Finally, we illustrate our techniques through both Monte Carlo simulations and an empirical application to 26 U.K. sectorial stock returns that confirms that their conditional distribution has fat tails.