Hill's estimator for the tail index of an ARMA model

Journal of Statistical Planning and Inference

Volumn 123, Issue 2, 2004, Pages 279-293

  Ling, Shiqing ^a   Peng, Liang ^b  

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

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

ARMA model; Hill's estimator; Optimal sample fraction; Regularly varying; Tail index

Indexed keywords

EID: 2142821372     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-3758(03)00151-4     Document Type: Article

References (24)

1. Billingsley P. Convergence of Probability Measures 1968 Wiley New York
2. Brockwell P. Davis R. Time Series: Theory and Methods 2nd Edition 1991 Springer New York
3. Danielsson J. de Haan L. Peng L. de Vries C.G. Using a bootstrap method to choose the sample fraction in the tail index estimation J. Multivariate Anal. 76 2001 226-248
4. Datta S. McCormick W.P. Inference for the tail parameters of a linear process with heavy tail innovations Ann. Inst. Statist. Math. 50 5 1998 337-359
5. Davis R.A. Gauss-Newton and M-Estimation for ARMA processes with infinite variance Stochastic Process. Appl. 63 1996 75-95
6. Drees H. Weighted approximations of tail processes under mixing conditions Ann. Appl. Probab. 10 4 2000 1274-1301
7. Drees H. Kaufmann E. Selecting the optimal sample fraction in univariate extreme value estimation Stochastic Process. Appl. 75 2 1998 149-172
8. Geluk, J., de Haan, L., 1987. Regular variation, extensions and Tauberian Theorems, CWI Tract 40, Amsterdam.
9. Geluk J. de Haan L. Resnick S. Starica C. Second order regular variation, convolution and the central limit theorem Stochastic Process. Appl. 9 1997 139-159
10. Geluk J. Peng L. An adaptive optimal estimate of the tail index for MA(1) time series Statist. Probab. Lett. 46 3 2000 217-227
11. Geluk J. Peng L. de Vries C.G. Convolutions of heavy tailed random variables and applications to portfolio diversification and MA(1) time series Adv. Appl. Probab. 32 4 2000 1011-1026
12. de Haan L. Peng L. Comparison of tail index estimators Statist. Neerlandica 52 1998 60-70
13. de Haan L. Resnick S.I. On asymptotic normality of the Hill estimator Stochastic Models 14 1998 849-867
14. Hill B. A simple approach to inference about the tail of a distribution Ann. Statist. 3 1975 1163-1174
15. Hsing T. On tail index estimation using dependent data Ann. Statist. 19 1991 1547-1569
16. Koul H.L. A weak convergence result useful in robust autoregression J. Statist. Plann. Inference 29 1991 1291-1308
17. Koul H.L. Levental S. Weak convergence of the residual empirical process in explosive autoregression Ann. Statist. 17 4 1989 1784-1794
18. Lee S. Wei C. On residual empirical processes of stochastic regression models with applications to time series Ann. Statist. 27 1 1999 237-261
19. Ling S. Weak convergence of the sequential empirical processes of residuals in nonstationary autoregressive models Ann. Statist. 26 2 1998 741-754
20. Mikosch T. Gadrich T. Klüppelburg C. Alder R.J. Parameter estimation for ARMA models with infinite variance innovations Ann. Statist. 23 1995 305-326
21. Resnick S. Starica C. Consistency of Hill's estimator for dependent data J. Appl. Probab. 32 1995 139-167
22. Resnick S. Starica C. Asymptotic behavior of Hill's estimator for autoregressive data Commun. Statist.-Stochastics Models 13 4 1997 21-703
23. Resnick S. Starica C. Tail index estimation for dependent data Ann. Appl. Probab. 8 1998 1156-1183
24. Rootzen H. Leadbetter M.R. de Haan L. On the distribution tail array sums for strongly mixing stationary sequences Ann. Appl. Probab. 8 1998 868-885