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Volumn 25, Issue 5, 1997, Pages 1805-1849

Heavy tail modeling and teletraffic data

Author keywords

Autoregressive processes; Consistency; Estimation; Heavy tails; Hill estimator; Independence; Linear programming; Parameter estimation; Poisson processes; Regular variation; Time series analysis; Weak convergence

Indexed keywords


EID: 0031512270     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1069362376     Document Type: Article
Times cited : (248)

References (82)
  • 1
    • 84981412776 scopus 로고
    • Nonnegative autoregressive processes
    • ANDEL, J. (1989). Nonnegative autoregressive processes. J. Time Ser. Anal. 10 1-11.
    • (1989) J. Time Ser. Anal. , vol.10 , pp. 1-11
    • Andel, J.1
  • 2
    • 0000911056 scopus 로고
    • Bootstrap of the mean in the infinite variance case
    • ATHREYA, K. (1987). Bootstrap of the mean in the infinite variance case. Ann. Statist. 15 724-731.
    • (1987) Ann. Statist. , vol.15 , pp. 724-731
    • Athreya, K.1
  • 4
    • 0029253909 scopus 로고
    • Long-range dependence in variable-bit rate video traffic
    • BERAN, J., SHERMAN, R., TAQQU, M. and WILLINGER, W. (1995). Long-range dependence in Variable-bit rate video traffic. IEEE Trans. Comm. 43 1566-1579.
    • (1995) IEEE Trans. Comm. , vol.43 , pp. 1566-1579
    • Beran, J.1    Sherman, R.2    Taqqu, M.3    Willinger, W.4
  • 5
    • 0003117761 scopus 로고
    • Consistent order determination for processes with infinite variance
    • BHANSALI, R. (1988). Consistent order determination for processes with infinite variance. J. Roy. Statist. Soc. Ser. B 50 46-60.
    • (1988) J. Roy. Statist. Soc. Ser. B , vol.50 , pp. 46-60
    • Bhansali, R.1
  • 10
    • 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. Cambridge Philos. Soc. 98 547-558.
    • (1985) Math. Proc. Cambridge Philos. Soc. , vol.98 , pp. 547-558
    • Csörgo, S.1    Mason, D.2
  • 11
    • 21344465385 scopus 로고
    • Bootstrap inference for a first order autoregression with positive innovations
    • DATTA, S. and MCCORMICK, W. (1995). Bootstrap inference for a first order autoregression with positive innovations. J. Amer. Statist. Soc. 90 1289-1301.
    • (1995) J. Amer. Statist. Soc. , vol.90 , pp. 1289-1301
    • Datta, S.1    McCormick, W.2
  • 12
    • 38249015513 scopus 로고
    • M-estimation for autoregressions with infinite variance
    • DAVIS, R., KNIGHT, K. and LIU, J. (1991). M-estimation for autoregressions with infinite variance. Stochastic Process. Appl. 40 145-180.
    • (1991) Stochastic Process. Appl. , vol.40 , pp. 145-180
    • Davis, R.1    Knight, K.2    Liu, J.3
  • 13
    • 45349110375 scopus 로고
    • Estimation for first-order autoregressive processes with positive or bounded innovations
    • DAVIS, R. and MCCORMICK, W. (1989). Estimation for first-order autoregressive processes with positive or bounded innovations. Stochastic Process. Appl. 31 237-250.
    • (1989) Stochastic Process. Appl. , vol.31 , pp. 237-250
    • Davis, R.1    McCormick, W.2
  • 14
    • 0000822729 scopus 로고
    • Tail estimates motivated by extreme value theory
    • DAVIS, R. and RESNICK, S. (1984). Tail estimates motivated by extreme value theory. Ann. Statist. 12 1467-1487.
    • (1984) Ann. Statist. , vol.12 , pp. 1467-1487
    • Davis, R.1    Resnick, S.2
  • 15
    • 0001568756 scopus 로고
    • Limit theory for moving averages of random variables with regularly varying tail probabilities
    • DAVIS, R. and RESNICK, S. (1985a). Limit theory for moving averages of random variables with regularly varying tail probabilities. Ann. Probab. 13 179-195.
    • (1985) Ann. Probab. , vol.13 , pp. 179-195
    • Davis, R.1    Resnick, S.2
  • 16
    • 0000613180 scopus 로고
    • More limit theory for the sample correlation function of moving averages
    • DAVIS, R. and RESNICK, S. (1985b). More limit theory for the sample correlation function of moving averages. Stochastic Process. Appl. 20 257-279.
    • (1985) Stochastic Process. Appl. , vol.20 , pp. 257-279
    • Davis, R.1    Resnick, S.2
  • 17
    • 0000074862 scopus 로고
    • Limit theory for the sample covariance and correlation functions of moving averages
    • DAVIS, R. and RESNICK, S. (1986). Limit theory for the sample covariance and correlation functions of moving averages. Ann. Statist. 14 533-558.
    • (1986) Ann. Statist. , vol.14 , pp. 533-558
    • Davis, R.1    Resnick, S.2
  • 18
    • 0030365344 scopus 로고    scopus 로고
    • Limit theory for bilinear processes with heavy tailed noise
    • Unpublished manuscript
    • DAVIS, R. and RESNICK, S. (1996). Limit theory for bilinear processes with heavy tailed noise. Unpublished manuscript. Ann. Appl. Probab. 6 1191-1210.
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 1191-1210
    • Davis, R.1    Resnick, S.2
  • 19
    • 0003248852 scopus 로고
    • On regular variation and its application to the weak convergence of sample extremes
    • Math. Centre, Amsterdam
    • DE HAAN, L. (1970). On regular variation and its application to the weak convergence of sample extremes. Math. Centre Tract 32. Math. Centre, Amsterdam.
    • (1970) Math. Centre Tract , vol.32
    • De Haan, L.1
  • 20
    • 0040404315 scopus 로고
    • Extreme value statistics
    • Econometric Institute, Erasmus Univ., Rotterdam
    • DE HAAN, L. (1991). Extreme value statistics. Lecture notes, Econometric Institute, Erasmus Univ., Rotterdam.
    • (1991) Lecture Notes
    • De Haan, L.1
  • 21
    • 0011028274 scopus 로고
    • Rate of convergence for bivariate extremes (total variation metric)
    • Econometric Institute, Erasmus Univ., Rotterdam
    • DE HAAN, L. and PENG, L. (1995a). Rate of convergence for bivariate extremes (total variation metric). Report 9465/A, Econometric Institute, Erasmus Univ., Rotterdam.
    • (1995) Report 9465/A
    • De Haan, L.1    Peng, L.2
  • 22
    • 0011028274 scopus 로고
    • Rate of convergence for bivariate extremes (uniform metric)
    • Econometric Institute, Erasmus Univ., Rotterdam
    • DE HAAN, L. and PENG, L. (1995b). Rate of convergence for bivariate extremes (uniform metric). Report 9466/A, Econometric Institute, Erasmus Univ., Rotterdam.
    • (1995) Report 9466/A
    • De Haan, L.1    Peng, L.2
  • 23
    • 0011039125 scopus 로고
    • Exact rates of convergence to a symmetric stable law
    • Econometric Institute, Erasmus Univ., Rotterdam
    • DE HAAN, L. and PENG, L. (1995c). Exact rates of convergence to a symmetric stable law. Report 9467/A, Econometric Institute, Erasmus Univ., Rotterdam.
    • (1995) Report 9467/A
    • De Haan, L.1    Peng, L.2
  • 24
    • 0040404333 scopus 로고
    • Comparison of tail index estimators
    • Econometric Institute, Erasmus Univ., Rotterdam
    • DE HAAN, L. and PENG, L. (1995d). Comparison of tail index estimators. Report 9464/A, Econometric Institute, Erasmus Univ., Rotterdam.
    • (1995) Report 9464/A
    • De Haan, L.1    Peng, L.2
  • 25
    • 0030485816 scopus 로고    scopus 로고
    • Second-order regular variation and rates of convergence in extreme-value theory
    • DE HAAN, L. and RESNICK, S. (1996). Second-order regular variation and rates of convergence in extreme-value theory. Ann. Probab. 24 97-124.
    • (1996) Ann. Probab. , vol.24 , pp. 97-124
    • De Haan, L.1    Resnick, S.2
  • 27
    • 0002952631 scopus 로고
    • Some results on the influence of extremes on the bootstrap
    • DEHEUVELS, P., MASON, D. and SHORACK, G. (1993). Some results on the influence of extremes on the bootstrap. Ann. Inst. H. Poincaré 29 83-103.
    • (1993) Ann. Inst. H. Poincaré , vol.29 , pp. 83-103
    • Deheuvels, P.1    Mason, D.2    Shorack, G.3
  • 28
    • 0001591373 scopus 로고
    • On the estimation of the extreme value index and large quantile estimation
    • DEKKERS, A. and DE HAAN, L. (1989). On the estimation of the extreme value index and large quantile estimation. Ann. Statist. 17 1795-1832.
    • (1989) Ann. Statist. , vol.17 , pp. 1795-1832
    • Dekkers, A.1    De Haan, L.2
  • 30
    • 0001760675 scopus 로고
    • A moment estimator for the index of an extreme value distribution
    • DEKKERS, A., EINMAHL, J. and DE HAAN, L. (1989). A moment estimator for the index of an extreme value distribution. Ann. Statist. 17 1833-1855.
    • (1989) Ann. Statist. , vol.17 , pp. 1833-1855
    • Dekkers, A.1    Einmahl, J.2    De Haan, L.3
  • 31
    • 0001115174 scopus 로고
    • Analyzing telecommunications traffic data from working common channel signaling subnetworks
    • Interface Foundation of North Americ̀a
    • DUFFY, D., MCINTOSH, A., ROSENSTEIN, M. and WILLINGER, W. (1993). Analyzing telecommunications traffic data from working common channel signaling subnetworks. In Proceedings of the 25th Interface, San Diego. Interface Foundation of North Americ̀a.
    • (1993) Proceedings of the 25th Interface, San Diego
    • Duffy, D.1    McIntosh, A.2    Rosenstein, M.3    Willinger, W.4
  • 33
    • 0030370303 scopus 로고    scopus 로고
    • Parameter estimation for moving averages with positive innovations
    • FEIGIN, P., KRATZ, M. and RESNICK, S. (1996). Parameter estimation for moving averages with positive innovations. Ann. Appl. Probab. 6 1157-1190.
    • (1996) Ann. Appl. Probab. , vol.6 , pp. 1157-1190
    • Feigin, P.1    Kratz, M.2    Resnick, S.3
  • 34
    • 84959967675 scopus 로고
    • Estimation for autoregressive processes with positive innovations
    • FEIGIN, P. and RESNICK, S. (1992). Estimation for autoregressive processes with positive innovations. Stochastic Model. 8 479-498.
    • (1992) Stochastic Model , vol.8 , pp. 479-498
    • Feigin, P.1    Resnick, S.2
  • 35
    • 38149147979 scopus 로고
    • Limit distributions for linear programming time series estimators
    • FEIGIN, P. and RESNICK, S. (1994). Limit distributions for linear programming time series estimators. Stochastic Process. Appl. 51 135-166.
    • (1994) Stochastic Process. Appl. , vol.51 , pp. 135-166
    • Feigin, P.1    Resnick, S.2
  • 37
    • 0031224028 scopus 로고    scopus 로고
    • Linear programming estimators and bootstrapping for heavy tailed phenomena
    • To appear. Available as TR1124.ps.Z at
    • FEIGIN, P. and RESNICK, S. (1997). Linear programming estimators and bootstrapping for heavy tailed phenomena. Adv. Appl. Probab. To appear. Available as TR1124.ps.Z at http://www.orie.cornell.edu/trlist/trlist.html.
    • (1997) Adv. Appl. Probab.
    • Feigin, P.1    Resnick, S.2
  • 38
    • 0029426717 scopus 로고
    • Testing for independence in heavy tailed and positive innovation time series
    • FEIGIN, P. RESNICK, S. and STǍRICǍ, C. (1995). Testing for independence in heavy tailed and positive innovation time series. Comm. Statist. Stochastic Models 11 587-612.
    • (1995) Comm. Statist. Stochastic Models , vol.11 , pp. 587-612
    • Feigin, P.1    Resnick, S.2    Stǎricǎ, C.3
  • 40
    • 0003326493 scopus 로고
    • Regular variation, extensions and Tauberian theorems
    • CWI, Amsterdam
    • GELUK, J. and DE HAAN, L. (1987). Regular variation, extensions and Tauberian theorems. CWI Tract 40, CWI, Amsterdam.
    • (1987) CWI Tract , vol.40
    • Geluk, J.1    De Haan, L.2
  • 41
    • 0031232406 scopus 로고    scopus 로고
    • Second order regular variation, convolution and the central limit theorem
    • To appear. Available as TR1133.ps.Z at
    • GELUK, J., DE HAAN, L., RESNICK, S. and STǍRICǍ, C. (1997). Second order regular variation, convolution and the central limit theorem. Stochastic Process. Appl. To appear. Available as TR1133.ps.Z at http://www.orie.cornell.edu/trlist/trlist.html.
    • (1997) Stochastic Process. Appl.
    • Geluk, J.1    De Haan, L.2    Resnick, S.3    Stǎricǎ, C.4
  • 42
    • 0000631354 scopus 로고
    • Necessary conditions for the bootstrap of the mean
    • GINÉ, E. and ZINN, J. (1989). Necessary conditions for the bootstrap of the mean. Ann. Statist. 17 684-691.
    • (1989) Ann. Statist. , vol.17 , pp. 684-691
    • Giné, E.1    Zinn, J.2
  • 45
    • 0002407801 scopus 로고
    • On some simple estimates of an exponent of regular variation
    • HALL, P. (1982). On some simple estimates of an exponent of regular variation. J. Roy. Statist. Soc. Ser. B 44 37-42.
    • (1982) J. Roy. Statist. Soc. Ser. B , vol.44 , pp. 37-42
    • Hall, P.1
  • 46
    • 0000753232 scopus 로고
    • Asymptotic properties of the bootstrap for heavy-tailed distributions
    • HALL, P. (1990). Asymptotic properties of the bootstrap for heavy-tailed distributions. Ann. Probab. 18 1342-1360.
    • (1990) Ann. Probab. , vol.18 , pp. 1342-1360
    • Hall, P.1
  • 47
    • 0039219877 scopus 로고    scopus 로고
    • Heavy tails and long range dependence in on/off processes and associated fluid models
    • To appear. Available as TR1144.ps.Z at
    • HEATH, D., RESNICK, S. and SAMORODNITSKY, G. (1997). Heavy tails and long range dependence in on/off processes and associated fluid models. Math. Oper. Res. To appear. Available as TR1144.ps.Z at http://www.orie.cornell.edu/trlist/trlist.html.
    • (1997) Math. Oper. Res.
    • Heath, D.1    Resnick, S.2    Samorodnitsky, G.3
  • 48
    • 0001263124 scopus 로고
    • A simple approach to inference about the tail of a distribution
    • HILL, B. (1975). A simple approach to inference about the tail of a distribution. Ann. Statist. 3 1163-1174.
    • (1975) Ann. Statist. , vol.3 , pp. 1163-1174
    • Hill, B.1
  • 49
    • 0000234372 scopus 로고
    • On tail estimation using dependent data
    • HSING, T. (1991). On tail estimation using dependent data. Ann. Statist. 19 1547-1569.
    • (1991) Ann. Statist. , vol.19 , pp. 1547-1569
    • Hsing, T.1
  • 50
    • 0000974326 scopus 로고
    • On the frequency of large stock returns: Putting booms and busts into perspective
    • JANSEN, D. and DE VRIES, C. (1991). On the frequency of large stock returns: putting booms and busts into perspective. Review of Economics and Statistics 73 18-24.
    • (1991) Review of Economics and Statistics , vol.73 , pp. 18-24
    • Jansen, D.1    De Vries, C.2
  • 52
    • 0002369099 scopus 로고
    • An invariance principle applicable to the bootstrap
    • (R. LePage and L. Billard, eds.). Wiley, New York
    • KINATEDER, J. (1992). An invariance principle applicable to the bootstrap. In Exploring the Limits of Bootstrap (R. LePage and L. Billard, eds.). Wiley, New York.
    • (1992) Exploring the Limits of Bootstrap
    • Kinateder, J.1
  • 53
    • 0001524152 scopus 로고
    • Order selection for autoregressions
    • KNIGHT, K. (1989a). Order selection for autoregressions. Ann. Statist. 17 824-840.
    • (1989) Ann. Statist. , vol.17 , pp. 824-840
    • Knight, K.1
  • 54
    • 0000660002 scopus 로고
    • On the bootstrap of the sample mean in the infinite variance case
    • KNIGHT, K. (1989b). On the bootstrap of the sample mean in the infinite variance case. Ann. Statist. 17 1168-1175.
    • (1989) Ann. Statist. , vol.17 , pp. 1168-1175
    • Knight, K.1
  • 56
    • 0000562848 scopus 로고
    • The qq estimator and heavy tails
    • KRATZ, M. and RESNICK, S. (1966). The qq estimator and heavy tails. Stochastic Models 12 699-724.
    • (1966) Stochastic Models , vol.12 , pp. 699-724
    • Kratz, M.1    Resnick, S.2
  • 58
    • 0004259421 scopus 로고
    • Bootstrapping signs
    • (R. LePage and L. Billard, eds.) Wiley, New York
    • LEPAGE, R. (1992). Bootstrapping signs. In Exploring the Limits of Bootstrap (R. LePage and L. Billard, eds.) 215-224. Wiley, New York.
    • (1992) Exploring the Limits of Bootstrap , pp. 215-224
    • Lepage, R.1
  • 59
    • 0000133909 scopus 로고
    • The impact of autocorrelations on queueing systems
    • LIVNY, M., MELAMED, B. and TSIOLIS, A. K. (1993). The impact of autocorrelations on queueing systems. Management Sciences 39 322-339.
    • (1993) Management Sciences , vol.39 , pp. 322-339
    • Livny, M.1    Melamed, B.2    Tsiolis, A.K.3
  • 60
    • 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. Probab. 10 754-764.
    • (1982) Ann. Probab. , vol.10 , pp. 754-764
    • Mason, D.1
  • 61
    • 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. Poincaré 24 491-506.
    • (1988) Ann. Inst. H. Poincaré , vol.24 , pp. 491-506
    • Mason, D.1
  • 62
    • 0010083335 scopus 로고
    • Weak convergence of the Hill estimator process
    • (J. Galambos, J. Lechner and E. Simiu, eds.) Kluwer, Dordrecht
    • MASON, D. and TUROVA, T. (1994). Weak convergence of the Hill estimator process. In Extreme Value Theory and Applications (J. Galambos, J. Lechner and E. Simiu, eds.) 419-432. Kluwer, Dordrecht.
    • (1994) Extreme Value Theory and Applications , pp. 419-432
    • Mason, D.1    Turova, T.2
  • 64
    • 21844492815 scopus 로고
    • Parameter estimation for ARMA models with infinite variance innovations
    • MIKOSCH, T., GADRICH, T., KLÜPPELBERG, C. and ADLER, R. (1995). Parameter estimation for ARMA models with infinite variance innovations. Ann. Statist. 23 305-326.
    • (1995) Ann. Statist. , vol.23 , pp. 305-326
    • Mikosch, T.1    Gadrich, T.2    Klüppelberg, C.3    Adler, R.4
  • 66
    • 0002095272 scopus 로고
    • Point processes, regular variation and weak convergence
    • RESNICK, S. (1986). Point processes, regular variation and weak convergence. Adv. in Appl. Probab. 18 66-138.
    • (1986) Adv. in Appl. Probab. , vol.18 , pp. 66-138
    • Resnick, S.1
  • 68
    • 0039219867 scopus 로고
    • Point processes and Tauberian theory
    • RESNICK, S. (1991). Point processes and Tauberian theory. Math. Sci. 16 83-106.
    • (1991) Math. Sci. , vol.16 , pp. 83-106
    • Resnick, S.1
  • 71
    • 0031099274 scopus 로고    scopus 로고
    • Performance decay in a single server exponential queuing model with long range dependence
    • To appear
    • RESNICK, S. and SAMORODNITSKY, G. (1997). Performance decay in a single server exponential queuing model with long range dependence. Oper. Res. To appear.
    • (1997) Oper. Res.
    • Resnick, S.1    Samorodnitsky, G.2
  • 72
    • 21844502279 scopus 로고
    • Consistency of Hill's estimator for dependent data
    • RESNICK, S. and STǍRICǍ, C. (1995). Consistency of Hill's estimator for dependent data. J. Appl. Probab. 32 139-167.
    • (1995) J. Appl. Probab. , vol.32 , pp. 139-167
    • Resnick, S.1    Stǎricǎ, C.2
  • 73
    • 0039219869 scopus 로고    scopus 로고
    • Preprint. Available by ftp from ftp.orie.cornell.edu as TR1158.ps.Z in directory /ftp/pub/techreps or at
    • RESNICK, S. and STǍRICǍ, C. (1996a). Smoothing the moment estimator of the extreme value parameter. Preprint. Available by ftp from ftp.orie.cornell.edu as TR1158.ps.Z in directory /ftp/pub/techreps or at http://www.orie.cornell.edu/trlist/trlist.html.
    • (1996) Smoothing the Moment Estimator of the Extreme Value Parameter
    • Resnick, S.1    Stǎricǎ, C.2
  • 75
    • 0000701834 scopus 로고    scopus 로고
    • Smoothing the Hill estimator
    • RESNICK, S. and STǍRICǍ, C. (1997). Smoothing the Hill estimator. J. Appl. Proabab. 29 271-293.
    • (1997) J. Appl. Proabab. , vol.29 , pp. 271-293
    • Resnick, S.1    Stǎricǎ, C.2
  • 77
    • 0013522037 scopus 로고
    • Tail and quantile estimation for strongly mixing stationary sequences
    • Center for Stochastic Processes, Dept. Statistics, Univ. North Carolina, Chapel Hill
    • ROOTZEN, H., LEADBETTER, M. and DE HAAN, L. (1990). Tail and quantile estimation for strongly mixing stationary sequences. Technical Report 292, Center for Stochastic Processes, Dept. Statistics, Univ. North Carolina, Chapel Hill.
    • (1990) Technical Report 292
    • Rootzen, H.1    Leadbetter, M.2    De Haan, L.3
  • 78
    • 0000974297 scopus 로고
    • On the structure of stationary stable processes
    • ROSIŃSKI, J. (1995). On the structure of stationary stable processes. Ann. Probab. 23 1163-1187.
    • (1995) Ann. Probab. , vol.23 , pp. 1163-1187
    • Rosiński, J.1
  • 80
    • 0038876140 scopus 로고
    • Uniform rates of convergence in extreme value theory
    • SMITH, R. (1982). Uniform rates of convergence in extreme value theory. Adv. in Appl. Probab. 14 543-565.
    • (1982) Adv. in Appl. Probab. , vol.14 , pp. 543-565
    • Smith, R.1
  • 81
    • 84972521562 scopus 로고
    • Self-similarity in high-speed packet traffic: Analysis and modeling of ethernet traffic measurements
    • WILLINGER, W., TAQQU, M., LELAND, W. and WILSON, D. (1995). Self-similarity in high-speed packet traffic: analysis and modeling of ethernet traffic measurements. Statist. Sci. 10 67-85.
    • (1995) Statist. Sci. , vol.10 , pp. 67-85
    • Willinger, W.1    Taqqu, M.2    Leland, W.3    Wilson, D.4
  • 82
    • 0031078972 scopus 로고    scopus 로고
    • Self-similarity through high-variability: Statistical analysis of Ethernet LAN traffic at the source level
    • WILLINGER, W., TAQQU, M., SHERMAN, R. and WILSON, D. (1997). Self-similarity through high-variability: statistical analysis of Ethernet LAN traffic at the source level. IEEE/ACM Transactions on Networking 5 71-96.
    • (1997) IEEE/ACM Transactions on Networking , vol.5 , pp. 71-96
    • Willinger, W.1    Taqqu, M.2    Sherman, R.3    Wilson, D.4


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