ASYMPTOTIC THEORY FOR A VECTOR ARMA-GARCH MODEL
Top Cited Papers
- 31 January 2003
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 19 (02), 280-310
- https://doi.org/10.1017/s0266466603192092
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.Keywords
This publication has 22 references indexed in Scilit:
- Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errorsThe Annals of Statistics, 1998
- On Fractionally Integrated Autoregressive Moving-Average Time Series Models With Conditional HeteroscedasticityJournal of the American Statistical Association, 1997
- On a multivariate conditional heteroscedastic modelBiometrika, 1997
- Multivariate Simultaneous Generalized ARCHEconometric Theory, 1995
- Tests of international CAPM with time‐varying covariancesJournal of Applied Econometrics, 1989
- Nested Reduced-Rank Autogressive Models for Multiple Time SeriesJournal of the American Statistical Association, 1988
- Invariant measures for Markov chains with no irreducibility assumptionsJournal of Applied Probability, 1988
- Generalized autoregressive conditional heteroskedasticityJournal of Econometrics, 1986
- Asymptotic Theory for ARCH Models: Estimation and TestingEconometric Theory, 1986
- Vector linear time series modelsAdvances in Applied Probability, 1976