Regression quantiles for unstable autoregressive models

Journal of Multivariate Analysis

Volumn 89, Issue 2, 2004, Pages 304-328

  Ling, Shiqing ^a   McAleer, Michael ^b  

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

^b UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Quantile estimation; Randomly weighted residual empirical process; Unit root; Unstable AR models

Indexed keywords

EID: 3242725654     PISSN: 0047259X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0047-259X(03)00127-1     Document Type: Article

References (34)

1. Bassett G.W. Koenker R.W. An empirical quantiles function for linear models with i.i.d. errors J. Amer. Statist. Assoc. 77 1982 407-415
2. Bickel P.J. Wichura M.J. Convergence for multiparameter stochastic processes and some applications Ann. Statist. 42 1971 1656-1670
3. Billingsley P. Convergence of Probability Measures 1968 Wiley New York
4. Chan N.H. Wei C.Z. Limiting distributions of least squares estimates of unstable autoregressive processes Ann. Statist. 16 1988 367-401
5. Cox D.D. Llatas I. Maximum likelihood type estimation for nearly nonstationary autoregressive time series Ann. Statist. 19 1991 1109-1128
6. Dickey D.A. Fuller W.A. Distribution of the estimators for autoregressive time series with a unit root J. Amer. Statist. Assoc. 74 1979 427-431
7. Dickey D.A. Hasza D.P. Fuller W.A. Testing for units roots in seasonal time series J. Amer. Statist. Assoc. 79 1984 355-367
8. Freedman D.A. On tail probability for martingales Ann. Probab. 3 1975 100-118
9. Hansen B.E. Rethinking the univariate approach to unit root testing. Using covariates to increase power. Trending multiple time series Econom. Theory 11 1995 1148-1171
10. Hasan M.N. Koenker R. Robust rank tests of the unit root hypothesis Econometrica 65 1997 61-133
11. Helland I.S. Central limit theorems for martingales with discrete or continuous time Scand. J. Statist. 9 1982 79-94
12. Herce M.A. Asymptotic theory of LAD estimation in a unit root process with finite variance errors Econom. Theory 12 1996 129-153
13. Jeganathan P. On the asymptotic behavior of least squares estimators in AR time series with roots near the unit circle Econom. Theory 7 1991 269-306
14. Koenker R.W. Bassett G.W. Regression quantiles Econometrica 46 1978 33-50
15. Koenker R.W. Bassett G.W. Robust tests for heteroscedasticity based on regression quantiles Econometrica 50 1982 43-61
16. Koenker R.W. D'Orey V. Algorithm AS 229: computing regression quantiles J. Roy. Statist. Soc. Ser. C 36 1987 383-393
17. Koenker R.W. D'Orey V. Remark AS229: computing regression quantiles J. Roy. Statist. Soc. Ser. C 43 1993 410-414
18. Koul H.L. A weak convergence result useful in robust autoregression J. Statist. Plann. Inference 29 1991 291-308
19. Koul H.L. Asymptotics of some estimators and sequential residual empiricals in nonlinear time series Ann. Statist. 24 1996 380-404
20. Koul H.L. Ossiander M. Weak convergence of randomly weighted dependent residual empiricals with applications to autoregression Ann. Statist. 22 1994 540-562
21. Koul H.L. Saleh A.K.Md.E. Autoregression quantiles and related rank scores processes Ann. Statist. 23 1995 670-689
22. Ling S. Weak convergence of the sequential empirical processes of residuals in nonstationary autoregressive models Ann. Statist. 26 1998 741-754
23. Ling S. Li W.K. Limiting distributions of maximum likelihood estimators for unstable ARMA time series with GARCH errors Ann. Statist. 26 1998 84-125
24. Ling S. Li W.K. Asymptotic inference of nonstationary fractional ARIMA models Econom. Theory 17 2001 738-764
25. Lucas A. Unit root tests based on M-estimators Econom. Theory 11 1995 331-346
26. van der Meer T. Pap G. van Zuijlen M.C.A. Asymptotic inference for nearly unstable AR(p) processes Econom. Theory 15 1999 184-217
27. Phillips P.C.B. Time series regression with a unit root Econometrica 55 1987 277-301
28. Phillips P.C.B. Partially identified econometric models Econom. Theory 5 1989 181-240
29. Phillips P.C.B. Durlauf S.N. Multiple time series regression with integrated processes Rev. Econom. Studies 53 1986 473-495
30. P.C.B. Phillips, Z. Xiao, A primer on unit root testing, J. Econom. Surv. 12 (1998) 423-470, in: M. McAleer, L. Oxley (Eds.), Practical Issues in Cointegration Analysis, Blackwell, Oxford, 1999.
31. Portnoy S. Koenker R.W. Adaptive L-estimation for linear models Ann. Statist. 17 1989 362-381
32. Ruppert D. Carroll R.J. Trimmed least squares estimation in the linear model J. Amer. Statist. Assoc. 75 1980 828-838
33. M.J. Straf, Weak convergence of stochastic process with several parameters, Proceedings of the Fourth Berkeley Symposium on Mathematics Statistics and Probability, Vol. 4, University of California Press, Berkeley, 1970, 187-221.
34. Truong-Van B. Larramendy I. Asymptotic distribution of least squares estimators for purely unstable ARMA (m,∞) Statistics 28 1996 307-346