Empirical likelihood for autoregressive models, with applications to unstable time series

Statistica Sinica

Volumn 12, Issue 2, 2002, Pages 387-407

  Chuang, Chin Shan ^a   Chan, Ngai Hang ^b  

^a Goldman Sachs Group   (United States)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Autoregressive models; Dual likelihood; Empirical likelihood; Unit root tests

Indexed keywords

EID: 0036556615     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (33)

1. Abadir, K. M. (1995). The limiting distribution of the t ratio under a unit root. Econom. Theory 11, 775-793.
2. Basawa, I. V., Mallik, A. K., McCormick, W. P., Reeves, J. H. and Taylor, R. L. (1991). Bootstrapping unstable first-order autoregressive processes. Ann. Statist. 19, 1098-1101.
3. Billingsley, P. (1995). Probability and Measure. 3rd edition. Wiley, New York.
4. Brockwell, P. J. and Davis, R. A. (1990). Time Series: Theory and Methods. 2nd edition. Springer-Verlag, New York.
5. Chan, N. H. (1988). Parameter inference for nearly nonstationary time series. J. Amer. Statist. Assoc. 83, 857-862.
6. Chan, N. H. and Terrin, N. (1995). Inference for unstable long-memory processes with applications to fractional unit root autoregressions. Ann. Statist. 23, 1662-1683.
7. Chan, N. H. and Wei, C. Z. (1987). Asymptotic inference for nearly nonstationary AR(1) processes. Ann. Statist. 15, 1050-1063.
8. Chan, N. H. and Wei, C. Z. (1988). Limiting distributions of least squares estimates of unstable autoregressive processes. Ann. Statist. 16, 367-401.
9. Chow, Y. (1965). Local convergence of martingales and the law of large numbers. Ann. Math. Statist. 36, 552-558.
10. Chuang, C. and Lai, T. L. (2000). Hybrid resampling methods for confidence intervals with discussion. Statist. Sinica 10, 1-50.
11. DiCiccio, T. J., Hall, P. and Romano, J. P. (1991). Empirical likelihood is Bartlett-correctable. Ann. Statist. 19, 1053-1061.
12. Dickey, D. A. and Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. J. Amer. Statist. Assoc. 74, 427-431.
13. Ferretti, N. and Romo, R. (1996). Unit root bootstrap tests for AR(1) models. Biometrika 83, 849-860.
14. Hall, P. and Heyde, C. C. (1980). Martingale Limit Theory and its Applications. Academic Press, New York.
15. Karatzas, I. and Shreve, S. (1991). Brownian Motion and Stochastic Calculus. 2nd edition. Springer, New York.
16. Kitamura, Y. (1997). Empirical likelihood methods for weakly dependent processes. Ann. Statist. 25, 2084-2102.
17. Kolaczyk, E. D. (1994). Empirical likelihood for generalized linear models. Statist. Sinica 4, 199-218.
18. Lai, T. L. and Wei, C. Z. (1982). Least squares estimates in stochastic regression models with applications to identification and control of dynamic systems. Ann. Statist. 10, 154-166.
19. Lai, T. L. and Wei, C. Z. (1985). Asymptotic properties of multivariate weighted sums with applications to stochastic regression in linear dynamic systems. In Multivariate Analysis-VI: Proceedings of the Sixth International Symposium on Multivariate Analysis (Edited by P. R. Krishnaiah), 375-394. North-Holland, Amsterdam.
20. Ling, S. and Li, W. K. (1998). Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroskedastic errors. Ann. Statist. 26, 84-125.
21. Monti, A. C. (1997). Empirical likelihood confidence regions in time series models. Biometrika 84, 395-405.
22. Mykland, P. A. (1994). Bartlett type identities for martingales. Ann. Statist. 22, 21-38.
23. Mykland, P. A. (1995). Dual likelihood. Ann. Statist. 23, 396-421.
24. Nielsen, B. (1997). Bartlett correction of the unit root test in autoregressive models. Biometrika 84, 500-504.
25. Owen, A. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika 75, 237-249.
26. Owen, A. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18, 90-120.
27. Owen, A. (1991). Empirical likelihood for linear models. Ann. Statist. 19, 1725-1747.
28. Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P. (1992). Numerical Recipes in C: The Art of Scientific Computing. 2nd edition. Cambridge University Press.
29. Qin, J. and Lawless, J. (1994). Empirical likelihood and general estimating equations. Ann. Statist. 22, 300-325.
30. Reinsel, G. (1997). Elements of Multivariate Time Series Analysis. 2nd edition. Springer-Verlag, New York.
31. Stock, J. H. (1991). Confidence intervals for the largest autoregressive root in U.S. macroeconomic time series. J. Monetary Econom. 29, 435-459.
32. White, J. S. (1958). The limiting distribution of the serial correlation coefficient in the explosive case. Ann. Math. Statist. 29, 1188-1197.
33. Wright, J. (1999). An empirical likelihood ratio test for a unit root, problem 99.2.1. Econom. Theory 15, 257.