Asymptotic Theory for a Vector Arma-garch Model

نویسندگان

  • SHIQING LING
  • MICHAEL MCALEER
  • Shiqing Ling
چکیده

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity ~ARMAGARCH! 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+

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تاریخ انتشار 2001