This paper investigates the asymptotic theory for a vector autoregressive moving average-generalized autoregressive conditional heteroskedasticity~ARMA-GARCH! model+ The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established+ Consistency of the quasimaximum-likelihood estimator~QMLE! is proved under only the second-order moment condition+ This consistency result is new, even for the univariate autoregressive conditional heteroskedasticity~ARCH! and GARCH models+ Moreover, the asymptotic normality of the QMLE for the vector ARCH model is obtained under only the second-order moment of the unconditional errors and the finite fourth-order moment of the conditional errors+ Under additional moment conditions, the asymptotic normality of the QMLE is also obtained for the vector ARMA-ARCH and ARMA-GARCH models and also a consistent estimator of the asymptotic covariance+
The rapid spread of new coronaviruses throughout China and the world in 2019-2020 has had a great impact on China's economic and social development. As the backbone of Chinese society, Chinese universities have made significant contributions to emergency risk management. Such contributions have been made primarily in the following areas: alumni resource collection, medical rescue and emergency management, mental health maintenance, control of staff mobility, and innovation in online education models. Through the support of these methods, Chinese universities have played a positive role in the prevention and control of the epidemic situation. However, they also face the problems of alumni's economic development difficulties, the risk of deadly infection to medical rescue teams and health workers, infection of teachers and students, and the unsatisfactory application of information technology in resolving the crisis. In response to these risks and emergency problems, we propose some corresponding solutions for public dissemination, including issues related to medical security, emergency research, professional assistance, positive communication, and hierarchical information-based teaching.
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