 ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODELShiqing Ling () and Michael McAleer Econometric Theory, 2003, vol. 19, issue 2, 280-310 Abstract: 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 quasi-maximum-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 authors thank the co-Editor, Bruce Hansen, and two referees for very helpful comments and suggestions and acknowledge the financial support of the Australian Research Council. Date: 2003 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:cup:etheor:v:19:y:2003:i:02:p:280-310_19 Access Statistics for this article More articles in Econometric Theory from Cambridge University Press Cambridge University Press, UPH, Shaftesbury Road, Cambridge CB2 8BS UK. |
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