Asymptotic Theory for a Vector ARMA-GARCH Model
This paper investigates the asymptotic theory for a vector ARMA-GARCH model. The conditions for the strict stationarity, ergodicity, and the higherorder 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 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, as well as a consistent estimator of the asymptotic covariance.
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- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- J. Pfanzagl, 1969. "On the measurability and consistency of minimum contrast estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 14(1), pages 249-272, December.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Tse, Y. K., 2000.
"A test for constant correlations in a multivariate GARCH model,"
Journal of Econometrics,
Elsevier, vol. 98(1), pages 107-127, September.
- Tom Doan, . "TSECCTEST: RATS procedure to perform Tse test for constant correlation in MV-GARCH model," Statistical Software Components RTS00214, Boston College Department of Economics.
- Tom Doan, . "RATS programs to replicate Tse's constant correlation GARCH test results," Statistical Software Components RTZ00161, Boston College Department of Economics.
- Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
- Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(01), pages 70-86, February.
- Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
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