Estimation for partially nonstationary multivariate autoregressive models with conditional heteroscedasticity

Biometrika

Volumn 88, Issue 4, 2001, Pages 1135-1152

  Li, W K ^a   Ling, Shiqing ^b   Wong, H ^c  

^a UNIVERSITY OF HONG KONG   (Hong Kong)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Brownian motion; Cointegration; Full rank and reduced rank maximum likelihood estimators; Least squares estimator; Multivariate ARCH process; Partially nonstationary; Unit root

Indexed keywords

EID: 0037862848     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/88.4.1135     Document Type: Article

References (31)

1. AHN, S. K. & REINSEL, G. C. (1990). Estimation for partially nonstationary multivariate models. J. Am. Statist. Assoc. 85, 813-23.
2. BOLLERSLEV, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Economet. 31, 307-27.
3. BOLLERSLEV, T., ENGLE, R. F. & NELSON, D. B. (1994). ARCH models. In Handbook of Econometrics, 4, Ed. R. Engle and D. McFadden, pp. 2959-3038. Amsterdam: North-Holland.
4. ENGLE, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of variance of U.K. inflation. Econometrica 50, 987-1008.
5. ENGLE, R. F. & GRANGER, C. W. J. (1987). Cointegrated and error correction: Representation, estimation and testing. Econometrica 55, 251-76.
6. ENGLE, R. F. & KRONER, K. F. (1995). Multivariate simultaneous generalized ARCH. Economet. Theory 11, 122-50.
7. FOUNTIS, N. G. & DICKEY, D. A. (1988). Testing for a unit root nonstationarity in multivariate time series. Ann. Statist. 17, 419-28.
8. HANSEN, H. & JUSELIUS, K. (1995). Cats in RATS. Evanston, IL: Estima.
9. HODGSON, D. J. (1998). Adaptive estimation of error correction models. Economet. Theory 14, 44-69.
10. JOHANSEN, S. (1988). Statistical analysis of cointegration vectors. J. Econ. Dynam. Contr. 12, 231-54.
11. JOHANSEN, S. (1992). Estimation and hypothesis testing of cointegrating vectors in Gaussian vector autoregressive models. Econometrica 59, 1551-80.
12. JOHANSEN, S. (1995). Likelihood-based Inference in Cointegrated Vector Autoregressive Models. New York: Oxford University Press.
13. KURTZ, T. G. & PROTTER, P. (1991). Weak limit theorems to stochastic integrals and stochastic differential equations. Ann. Prob. 19, 1035-70.
14. LI, C. W. & LI, W. K. (1996). On a double threshold autoregressive conditional heteroskedastic time series model. J. Appl. Economet. 11, 253-74.
15. LING, S. (1999). On the stationarity and the existence of moments of conditional heteroskedastic ARMA models. Statist. Sinica 9, 1119-30.
16. LING, S. & DENG, W. C. (1993). Parametric estimate of multivariate autoregressive models with conditional heterocovariance matrix errors. Acta Math. Appl. Sinica 16, 517-33.
17. LING, S. & LI, W. K. (1998). Limiting distributions of maximum likelihood estimators for unstable ARMA models with GARCH errors. Ann. Statist. 26, 84-125.
18. LING, S. & MCALEER, M. (2002). On adaptive estimation in nonstationary ARMA models with GARCH errors. Ann. Statist. To appear.
19. LUCAS, A. (1997). Cointegration testing using pseudolikelihood ratio tests. Economet. Theory 13, 149-69.
20. LUTKEPOHL, H. (1993). Introduction to Multiple Time Series Analysis. New York: Springer-Verlag.
21. MADDALA, G. S. & KIM, I-M. (1998). Unit Roots, Cointegration and Structural Change. Cambridge: Cambridge University Press.
22. NICHOLLS, D. F. & QUINN, B. G. (1982). Random Coefficient Autoregressive Model: An Introduction, Lecture Notes in Statistics, 11. New York: Springer.
23. RAHBEK, A. & MOSCONI, R. (1999). Cointegration rank inference with stationary regressors in VAR models. Economet. J. 2, 76-91.
24. REINSEL, G. C. & AHN, S. K. (1992). Vector AR models with unit root and reduced rank structure: estimation, likelihood ratio test, and forecasting. J. Time Ser. Anal. 13, 353-75.
25. SEO, B. (1998). Statistical inference on cointegration rank in error correction models with stationary covariates. J. Economet. 85, 339-85.
26. SEO, B. (1999). Distribution theory for unit root tests with conditional heteroskedasticity. J. Economet. 91, 113-44.
27. STOCK, J. H. & WATSON, M. W. (1993). A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61, 783-820.
28. TSAY, R. S. (1987). Conditional heteroscedastic time series models. J. Am. Statist. Assoc. 82, 590-604.
29. WOOLDRIDGE, J. M. & WHITE, H. (1988). Some invariance principles and central limit theorems for dependent heterogeneous processes. Economet. Theory 4, 210-30.
30. WONG, H. & Li, W. K. (1997). On a multivariate conditional heteroscedasticity model. Biometrika 84, 111-23.
31. YAP, S. F. & REINSEL, G. C. (1995). Estimation and testing for unit roots in a partially nonstationary vector autoregressive moving average model. J. Am. Statist. Assoc. 90, 253-67.