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Volumn 41A, Issue , 2004, Pages 191-212

On the foundations of multivariate heavy-tail analysis

Author keywords

Angular measure; Asymptotic independence; Extremal dependence; Heavy tails; Regular variation

Indexed keywords


EID: 33845792425     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1239/jap/1082552199     Document Type: Article
Times cited : (46)

References (53)
  • 2
    • 0036392461 scopus 로고    scopus 로고
    • A characterization of multivariate regular variation
    • Basrak, B., Davis, R. A. and Mikosch, T. (2002). A characterization of multivariate regular variation. Ann. Appl. Prob. 12, 908-920.
    • (2002) Ann. Appl. Prob. , vol.12 , pp. 908-920
    • Basrak, B.1    Davis, R.A.2    Mikosch, T.3
  • 5
    • 42449156579 scopus 로고
    • Generalized autoregressive conditional heteroskedasticity
    • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. J. Econometrics 31,307-327.
    • (1986) J. Econometrics , vol.31 , pp. 307-327
    • Bollerslev, T.1
  • 6
    • 34848900983 scopus 로고
    • ARCH modeling in finance: A review of the theory and empirical evidence
    • Bollerslev, T., Chow, R. Y. and Kroner, K. F. (1992). ARCH modeling in finance: a review of the theory and empirical evidence. J. Econometrics 52, 5-59.
    • (1992) J. Econometrics , vol.52 , pp. 5-59
    • Bollerslev, T.1    Chow, R.Y.2    Kroner, K.F.3
  • 8
    • 0030149554 scopus 로고    scopus 로고
    • Self-similarity in world wide web traffic: Evidence and possible causes
    • Crovella, M. and Bestavros, A. (1996). Self-similarity in world wide web traffic: evidence and possible causes. Performance Evaluation Rev. 24, 160-169.
    • (1996) Performance Evaluation Rev , vol.24 , pp. 160-169
    • Crovella, M.1    Bestavros, A.2
  • 9
    • 0031383380 scopus 로고    scopus 로고
    • Self-similarity in world wide web traffic: Evidence and possible causes
    • Crovella, M. and Bestavros, A. (1997). Self-similarity in world wide web traffic: evidence and possible causes. IEEE/ACM Trans. Networking 5, 835-846.
    • (1997) IEEE/ACM Trans. Networking , vol.5 , pp. 835-846
    • Crovella, M.1    Bestavros, A.2
  • 11
    • 84971138745 scopus 로고
    • Central limit theorems for sums of extreme values
    • Csörgo, S. and Mason, D. (1985). Central limit theorems for sums of extreme values. Math. Proc. Camb. Phil. Soc. 98, 547-558.
    • (1985) Math. Proc. Camb. Phil. Soc. , vol.98 , pp. 547-558
    • Csörgo, S.1    Mason, D.2
  • 12
    • 0000857049 scopus 로고
    • Kernel estimates for the tail index of a distribution
    • Csörgo, S, Deheuvels, P. and Mason, D. (1985). Kernel estimates for the tail index of a distribution. Ann. Statist. 13, 1050-1077.
    • (1985) Ann. Statist. , vol.13 , pp. 1050-1077
    • Csörgo, S.1    Deheuvels, P.2    Mason, D.3
  • 14
    • 0032264526 scopus 로고    scopus 로고
    • The sample autocorrelations of heavy-tailed processes with applications to ARCH
    • Davis, R. A. and Mikosch, T. (1998). The sample autocorrelations of heavy-tailed processes with applications to ARCH. Ann. Statist. 26, 2049-2080.
    • (1998) Ann. Statist. , vol.26 , pp. 2049-2080
    • Davis, R.A.1    Mikosch, T.2
  • 15
    • 0006002068 scopus 로고
    • Integrals and derivatives of regularly varying functions in Rd and domains of attraction of stable distributions, II
    • d and domains of attraction of stable distributions, II. Stoch. Process. Appl. 16, 157-170.
    • (1984) Stoch. Process. Appl. , vol.16 , pp. 157-170
    • De Haan, L.1    Omey, E.2
  • 16
    • 0000732708 scopus 로고
    • Limit theory for multivariate sample extremes
    • DeHaan, L. and Resnick, S. I. (1977). Limit theory for multivariate sample extremes. Z. Wahrscheinlichkeitsth. 40, 317-337.
    • (1977) Z. Wahrscheinlichkeitsth. , vol.40 , pp. 317-337
    • Dehaan, L.1    Resnick, S.I.2
  • 17
    • 0009165582 scopus 로고
    • Derivatives of regularly varying functions in Rd and domains of attraction of stable distributions
    • d and domains of attraction of stable distributions. Stoch. Process. Appl. 8, 349-355.
    • (1978) Stoch. Process. Appl. , vol.8 , pp. 349-355
    • De Haan, L.1    Resnick, S.I.2
  • 18
    • 0040620195 scopus 로고
    • On regular variation of probability densities
    • De Haan, L. and Resnick, S. I. (1987). On regular variation of probability densities. Stoch. Process. Appl. 25, 83-95.
    • (1987) Stoch. Process. Appl. , vol.25 , pp. 83-95
    • De Haan, L.1    Resnick, S.I.2
  • 19
    • 0011515738 scopus 로고    scopus 로고
    • On asymptotic normality of the Hill estimator
    • De Haan, L. and Resnick, S. I. (1998). On asymptotic normality of the Hill estimator. Stoch. Models 14, 849-867.
    • (1998) Stoch. Models , vol.14 , pp. 849-867
    • De Haan, L.1    Resnick, S.I.2
  • 23
    • 0001115174 scopus 로고
    • Analyzing telecommunications traffic data from working common channel signaling subnetworks
    • (Proc. 25th Symp. Interface San Diego, CA), eds M. E. Tarter and M. D. Lock
    • Duffy, D. E., McIntosh, A. A., Rosenstein, M. and Willinger, W. (1993). Analyzing telecommunications traffic data from working common channel signaling subnetworks. In Computing Science and Statistics Interface (Proc. 25th Symp. Interface San Diego, CA), eds M. E. Tarter and M. D. Lock, pp. 156-165.
    • (1993) Computing Science and Statistics Interface , pp. 156-165
    • Duffy, D.E.1    McIntosh, A.A.2    Rosenstein, M.3    Willinger, W.4
  • 24
    • 0035470895 scopus 로고    scopus 로고
    • Nonparametric estimation of the spectral measure of an extreme value distribution
    • Einmahl, J., de Haan, L. and Piterbarg, V (2001). Nonparametric estimation of the spectral measure of an extreme value distribution. Ann. Statist. 29, 1401-1423.
    • (2001) Ann. Statist. , vol.29 , pp. 1401-1423
    • Einmahl, J.1    De Haan, L.2    Piterbarg, V.3
  • 25
    • 0000051984 scopus 로고
    • Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation
    • Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987-1008.
    • (1982) Econometrica , vol.50 , pp. 987-1008
    • Engle, R.F.1
  • 27
    • 0003673620 scopus 로고
    • (CWI Tract 40). Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam
    • Geluk, J. L. and de Haan, L. (1987). Regular Variation, Extensions and Tauberian Theorems (CWI Tract 40). Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Amsterdam.
    • (1987) Regular Variation, Extensions and Tauberian Theorems
    • Geluk, J.L.1    De Haan, L.2
  • 28
    • 0000732230 scopus 로고
    • Implicit renewal theory and tails of solutions of random equations
    • Goldie, C. M. (1991). Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Prob. 1, 126-166.
    • (1991) Ann. Appl. Prob. , vol.1 , pp. 126-166
    • Goldie, C.M.1
  • 29
    • 2942672026 scopus 로고
    • Random difference equations and renewal theory for products of random matrices
    • Kesten, H. (1973). Random difference equations and renewal theory for products of random matrices. Acta Math. 131, 207-248.
    • (1973) Acta Math , vol.131 , pp. 207-248
    • Kesten, H.1
  • 30
    • 0030384024 scopus 로고    scopus 로고
    • On the relationship between file sizes, transport protocols, and self-similar network traffic. In
    • Crovella, M., Kim, G. and Park, K. (1996). On the relationship between file sizes, transport protocols, and self-similar network traffic. In Proc. 4th Internat. Conf. Network Protocols (ICNP’96), pp. 171-180.
    • (1996) Proc. 4Th Internat. Conf. Network Protocols (ICNP’96) , pp. 171-180
    • Crovella, M.1    Kim, G.2    Park, K.3
  • 31
    • 0002198227 scopus 로고    scopus 로고
    • (1993). Statistical analysis of high timeresolution ethernet Lan traffic measurements
    • (Proc. 25th Symp. Interface, San Diego, CA), eds M. E. Taylor and M. D. Lock
    • Leland, W. E., Taqqu, M. S., Willinger, W. and Wilson, D. V. (1993). Statistical analysis of high timeresolution ethernet Lan traffic measurements. In Computer Science and Statistics Interface (Proc. 25th Symp. Interface, San Diego, CA), eds M. E. Taylor and M. D. Lock, pp. 146-155.
    • Computer Science and Statistics Interface , pp. 146-155
    • Leland, W.E.1    Taqqu, M.S.2    Willinger, W.3    Wilson, D.V.4
  • 32
    • 0000782528 scopus 로고
    • Laws of large numbers for sums of extreme values
    • Mason, D. (1982). Laws of large numbers for sums of extreme values. Ann. Prob. 10, 754-764.
    • (1982) Ann. Prob. , vol.10 , pp. 754-764
    • Mason, D.1
  • 33
    • 0001411703 scopus 로고
    • A strong invariance theorem for the tail empirical process
    • Mason, D. (1988). A strong invariance theorem for the tail empirical process. Ann. Inst. H. Poincare Prob. Statist. 24, 491-506.
    • (1988) Ann. Inst. H. Poincare Prob. Statist. , vol.24 , pp. 491-506
    • Mason, D.1
  • 34
    • 0010083335 scopus 로고
    • Weak convergence of the Hill estimator process
    • J. Galambos, J. Lechner, and E. Simiu, Kluwer, Dordrecht
    • Mason, D. and Turova, T. (1994). Weak convergence of the Hill estimator process. In Extreme Value Theory and Applications, eds J. Galambos, J. Lechner, and E. Simiu, Kluwer, Dordrecht, pp. 419-432.
    • (1994) Extreme Value Theory and Applications , pp. 419-432
    • Mason, D.1    Turova, T.2
  • 35
    • 84940499148 scopus 로고    scopus 로고
    • Modeling dependence and tails of financial time series
    • (SemStat, Gothenburg, 2001), eds B. Finkenstadt and H. Rootzen, Chapman and Hall/CRC, Boca Raton, FL
    • Mikosch, T. (2003). Modeling dependence and tails of financial time series. In Extreme Values in Finance, Telecommunications, and the Environment (SemStat, Gothenburg, 2001), eds B. Finkenstadt and H. Rootzen, Chapman and Hall/CRC, Boca Raton, FL, pp. 185-286.
    • (2003) Extreme Values in Finance, Telecommunications, and the Environment , pp. 185-286
    • Mikosch, T.1
  • 37
    • 0000569678 scopus 로고
    • Tail equivalence and its applications
    • Resnick, S. (1971). Tail equivalence and its applications. J. Appl. Prob. 8, 136-156.
    • (1971) J. Appl. Prob. , vol.8 , pp. 136-156
    • Resnick, S.1
  • 38
    • 0002095272 scopus 로고
    • Point processes, regular variation and weak convergence
    • Resnick, S. (1986). Point processes, regular variation and weak convergence. Adv. Appl Prob. 18, 66-138.
    • (1986) Adv. Appl Prob. , vol.18 , pp. 66-138
    • Resnick, S.1
  • 40
    • 85011519678 scopus 로고    scopus 로고
    • Discussion of the Danish data on large fire insurance losses
    • Resnick, S. (1997). Discussion of the Danish data on large fire insurance losses. ASTIN Bull. 27, 139-151.
    • (1997) ASTIN Bull , vol.27 , pp. 139-151
    • Resnick, S.1
  • 41
    • 0031512270 scopus 로고    scopus 로고
    • Heavy tail modeling and teletraffic data
    • Resnick, S. (1997). Heavy tail modeling and teletraffic data. Ann. Statist. 25, 1805-1869.
    • (1997) Ann. Statist. , vol.25 , pp. 1805-1869
    • Resnick, S.1
  • 43
    • 21844502279 scopus 로고
    • Consistency of Hill’s estimator for dependent data
    • Resnick, S. and Starica, C. (1995). Consistency of Hill’s estimator for dependent data. J. Appl. Prob. 32, 139-167.
    • (1995) J. Appl. Prob. , vol.32 , pp. 139-167
    • Resnick, S.1    Starica, C.2
  • 44
    • 0008697956 scopus 로고    scopus 로고
    • Asymptotic behavior of Hill’s estimator for autoregressive data
    • Resnick, S. and Starica, C. (1997). Asymptotic behavior of Hill’s estimator for autoregressive data. Stoch. Models 13, 703-723.
    • (1997) Stoch. Models , vol.13 , pp. 703-723
    • Resnick, S.1    Starica, C.2
  • 45
    • 0000701834 scopus 로고    scopus 로고
    • Smoothing the Hill estimator
    • Resnick, S. and Starica, C. (1997). Smoothing the Hill estimator. Adv. Appl. Prob. 29, 271-293.
    • (1997) Adv. Appl. Prob. , vol.29 , pp. 271-293
    • Resnick, S.1    Starica, C.2
  • 46
    • 0038979538 scopus 로고    scopus 로고
    • Tail index estimation for dependent data
    • Resnick, S. and Starica, C. (1998). Tail index estimation for dependent data. Ann. Appl. Prob. 8, 1156-1183.
    • (1998) Ann. Appl. Prob. , vol.8 , pp. 1156-1183
    • Resnick, S.1    Starica, C.2
  • 47
    • 0004263072 scopus 로고
    • (Lecture Notes Math. 508). Springer, NewYork
    • Seneta, E. (1976). Regularly Varying Functions (Lecture Notes Math. 508). Springer, NewYork.
    • (1976) Regularly Varying Functions
    • Seneta, E.1
  • 48
    • 0040920042 scopus 로고    scopus 로고
    • Estimating failure probability when failure is rare: Multidimensional case. Doctoral Thesis, Tinbergen Institute
    • Sinha, A. K. (1997). Estimating failure probability when failure is rare: multidimensional case. Doctoral Thesis, Tinbergen Institute, Erasmus University Rotterdam.
    • (1997) Erasmus University Rotterdam
    • Sinha, A.K.1
  • 49
    • 0002234093 scopus 로고    scopus 로고
    • Multivariate extremes for models with constant conditional correlations
    • Starica, C. (1999). Multivariate extremes for models with constant conditional correlations. J. Empirical Finance 6, 515-553.
    • (1999) J. Empirical Finance , vol.6 , pp. 515-553
    • Starica, C.1
  • 50
    • 17544364517 scopus 로고    scopus 로고
    • Multivariate extremes for models with constant conditional correlations
    • ed P. Embrechts, Risk Books, London
    • Starica, C. (2000). Multivariate extremes for models with constant conditional correlations. In Extremes and Integrated Risk Management, ed P. Embrechts, Risk Books, London, pp. 515-553.
    • (2000) Extremes and Integrated Risk Management , pp. 515-553
    • Starica, C.1
  • 51
    • 0001565579 scopus 로고
    • Onastochastic difference equationandarepresentation of non-negativeinfinitelydivisible random variables
    • Vervaat, W. (1979). Onastochastic difference equationandarepresentation of non-negativeinfinitelydivisible random variables. Adv. Appl Prob. 11, 750-783.
    • (1979) Adv. Appl Prob. , vol.11 , pp. 750-783
    • Vervaat, W.1
  • 52
    • 84972521562 scopus 로고
    • Self-similarityinhigh-speedpackettraffic: Analysis and modelling of ethernet traffic measurements
    • Willinger, W., Taqqu, M. S., Leland, M. and Wilson, D. (1995). Self-similarityinhigh-speedpackettraffic: analysis and modelling of ethernet traffic measurements. Statist. Sci. 10, 67-85.
    • (1995) Statist. Sci. , vol.10 , pp. 67-85
    • Willinger, W.1    Taqqu, M.S.2    Leland, M.3    Wilson, D.4
  • 53
    • 85013592037 scopus 로고
    • Self-similarity through high variability: Statistical analysis of ethernet lan traffic at the source level
    • Willinger, W., Taqqu, M. S., Leland, M. and Wilson, D. (1995). Self-similarity through high variability: statistical analysis of ethernet lan traffic at the source level. Comput. Commun. Rev. 25, 100-113.
    • (1995) Comput. Commun. Rev. , vol.25 , pp. 100-113
    • Willinger, W.1    Taqqu, M.S.2    Leland, M.3    Wilson, D.4


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