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Volumn 139, Issue 6, 2009, Pages 2091-2110

On functional central limit theorems for dependent, heterogeneous arrays with applications to tail index and tail dependence estimation

Author keywords

Extremal near epoch dependence; Functional central limit theorem; Hill estimator; Tail arrays; Tail dependence; Tail empirical process; Tail quantile process

Indexed keywords


EID: 60949110789     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2008.09.005     Document Type: Article
Times cited : (24)

References (62)
  • 1
    • 0036392461 scopus 로고    scopus 로고
    • A characterization of multivariate regular variation
    • Basrak B., Davis R.A., and Mikosch T. A characterization of multivariate regular variation. Ann. Appl. Prob. 12 (2002) 908-920
    • (2002) Ann. Appl. Prob. , vol.12 , pp. 908-920
    • Basrak, B.1    Davis, R.A.2    Mikosch, T.3
  • 2
    • 0000182551 scopus 로고
    • Extremes in non-life insurance
    • Galambos J., Lechner J., and Simui E. (Eds), Kluwer, Dordrecht
    • Beirlant J., Teugels J., and Vynckier P. Extremes in non-life insurance. In: Galambos J., Lechner J., and Simui E. (Eds). Extreme Value Theory and Applications (1994), Kluwer, Dordrecht
    • (1994) Extreme Value Theory and Applications
    • Beirlant, J.1    Teugels, J.2    Vynckier, P.3
  • 3
    • 0000472754 scopus 로고
    • Convergence criteria for multiparameter stochastic processes and some applications
    • Bickel P.J., and Wichura M.J. Convergence criteria for multiparameter stochastic processes and some applications. Ann. Math. Statist. 42 (1971) 1656-1670
    • (1971) Ann. Math. Statist. , vol.42 , pp. 1656-1670
    • Bickel, P.J.1    Wichura, M.J.2
  • 7
    • 0036003734 scopus 로고    scopus 로고
    • Mixing and moment properties of various GARCH and stochastic volatility models
    • Carrasco, and Chen. Mixing and moment properties of various GARCH and stochastic volatility models. Econometric Theory 18 (2002) 17-39
    • (2002) Econometric Theory , vol.18 , pp. 17-39
    • Carrasco1    Chen2
  • 8
    • 0001870612 scopus 로고    scopus 로고
    • Dependence measures for extreme value analysis
    • Coles S., Heffernan J., and Tawn J. Dependence measures for extreme value analysis. Extremes 2 (1999) 339-365
    • (1999) Extremes , vol.2 , pp. 339-365
    • Coles, S.1    Heffernan, J.2    Tawn, J.3
  • 10
    • 84971971019 scopus 로고
    • The central limit theorem for globally non-stationary near-epoch-dependent functions of mixing processes
    • Davidson J. The central limit theorem for globally non-stationary near-epoch-dependent functions of mixing processes. Econometric Theory 8 (1992) 313-334
    • (1992) Econometric Theory , vol.8 , pp. 313-334
    • Davidson, J.1
  • 12
    • 0742324055 scopus 로고    scopus 로고
    • Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model
    • Davidson J. Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model. J. Bus. Econ. Statist. 22 (2004) 16-29
    • (2004) J. Bus. Econ. Statist. , vol.22 , pp. 16-29
    • Davidson, J.1
  • 13
    • 0034367314 scopus 로고    scopus 로고
    • The functional central limit theorem and weak convergence to stochastic integrals
    • Davidson J., and de Jong R.M. The functional central limit theorem and weak convergence to stochastic integrals. Econometric Theory 16 (2000) 621-642
    • (2000) Econometric Theory , vol.16 , pp. 621-642
    • Davidson, J.1    de Jong, R.M.2
  • 14
    • 0031505926 scopus 로고    scopus 로고
    • Central limit theorems for dependent heterogeneous random variables
    • de Jong R.M. Central limit theorems for dependent heterogeneous random variables. Econometric Theory 13 (1997) 353-367
    • (1997) Econometric Theory , vol.13 , pp. 353-367
    • de Jong, R.M.1
  • 16
    • 33747334833 scopus 로고    scopus 로고
    • Tail empirical processes under mixing conditions
    • Dehling H., Mikosch T., and Sørensen's M. (Eds), Birkhauser, Berlin
    • Drees H. Tail empirical processes under mixing conditions. In: Dehling H., Mikosch T., and Sørensen's M. (Eds). Empirical Process Techniques for Dependent Data (2002), Birkhauser, Berlin
    • (2002) Empirical Process Techniques for Dependent Data
    • Drees, H.1
  • 17
    • 22244474071 scopus 로고    scopus 로고
    • On maximum likelihood estimation of the extreme value index
    • Drees H., Ferreira A., and de Haan L. On maximum likelihood estimation of the extreme value index. Ann. Appl. Probab. 14 (2004) 1179-1201
    • (2004) Ann. Appl. Probab. , vol.14 , pp. 1179-1201
    • Drees, H.1    Ferreira, A.2    de Haan, L.3
  • 18
    • 38249012933 scopus 로고
    • Limit theorems for tail processes with application to intermediate quantile estimation
    • Einmahl J.H.J. Limit theorems for tail processes with application to intermediate quantile estimation. J. Statist. Plann. Inference 32 (1992) 127-145
    • (1992) J. Statist. Plann. Inference , vol.32 , pp. 127-145
    • Einmahl, J.H.J.1
  • 19
    • 33744817636 scopus 로고    scopus 로고
    • Asymptotic normality of extreme value estimators on C[0,1]
    • Einmahl J.H.J., and Lin T. Asymptotic normality of extreme value estimators on C[0,1]. Ann. Statist. 34 (2006) 469-492
    • (2006) Ann. Statist. , vol.34 , pp. 469-492
    • Einmahl, J.H.J.1    Lin, T.2
  • 21
  • 24
    • 0003062471 scopus 로고
    • Slow variation with remainder: theory and applications
    • Goldie C.M., and Smith R.L. Slow variation with remainder: theory and applications. Quart. J. Math. 38 (1987) 45-71
    • (1987) Quart. J. Math. , vol.38 , pp. 45-71
    • Goldie, C.M.1    Smith, R.L.2
  • 25
    • 0001618329 scopus 로고
    • On asymptotic normality of Hill's estimator for the exponent of regular variation
    • Haeusler E., and Teugels J.L. On asymptotic normality of Hill's estimator for the exponent of regular variation. Ann. Statist. 13 (1985) 743-756
    • (1985) Ann. Statist. , vol.13 , pp. 743-756
    • Haeusler, E.1    Teugels, J.L.2
  • 26
    • 0002407801 scopus 로고
    • On Some Estimates of an Exponent of Regular Variation
    • Hall P. On Some Estimates of an Exponent of Regular Variation. J. Roy. Statisti. Soc. Ser. B 44 (1982) 37-42
    • (1982) J. Roy. Statisti. Soc. Ser. B , vol.44 , pp. 37-42
    • Hall, P.1
  • 28
    • 0000817285 scopus 로고
    • Adaptive estimates of parameters of regular variation
    • Hall P., and Welsh A.H. Adaptive estimates of parameters of regular variation. Ann. Statist. 13 (1985) 331-341
    • (1985) Ann. Statist. , vol.13 , pp. 331-341
    • Hall, P.1    Welsh, A.H.2
  • 29
    • 3542996305 scopus 로고    scopus 로고
    • A conditional approach to multivariate extreme values
    • Heffernan J., and Tawn J.A. A conditional approach to multivariate extreme values. J. Roy. Statist. Soc. Ser. B 66 (2004) 497-546
    • (2004) J. Roy. Statist. Soc. Ser. B , vol.66 , pp. 497-546
    • Heffernan, J.1    Tawn, J.A.2
  • 30
    • 0001263124 scopus 로고
    • A simple general approach to inference about the tail of a distribution
    • Hill B.M. A simple general approach to inference about the tail of a distribution. Ann. Math. Statist. 3 (1975) 1163-1174
    • (1975) Ann. Math. Statist. , vol.3 , pp. 1163-1174
    • Hill, B.M.1
  • 31
    • 33751219120 scopus 로고    scopus 로고
    • Working paper, Department of Economics, University of North Carolina, Chapel Hill. Available at
    • Hill, J.B., 2005. On tail index estimation for dependent, heterogenous data. Working paper, Department of Economics, University of North Carolina, Chapel Hill. Available at: 〈www.unc.edu/∼jbhill/hill_het_dep.pdf〉.
    • (2005) On tail index estimation for dependent, heterogenous data
    • Hill, J.B.1
  • 33
    • 60949113018 scopus 로고    scopus 로고
    • Working paper, Department of Economics, University of North Carolina, Chapel Hill. Available at
    • Hill, J.B., 2007b. Robust non-parametric tests of extremal dependence. Working paper, Department of Economics, University of North Carolina, Chapel Hill. Available at: 〈www.unc.edu/∼jbhill/extremal_spillover.pdf〉.
    • (2007) Robust non-parametric tests of extremal dependence
    • Hill, J.B.1
  • 36
    • 0000234372 scopus 로고
    • On tail index estimation using dependent data
    • Hsing T. On tail index estimation using dependent data. Ann. Statist. 19 (1991) 1547-1569
    • (1991) Ann. Statist. , vol.19 , pp. 1547-1569
    • Hsing, T.1
  • 37
    • 0033164330 scopus 로고    scopus 로고
    • On the asymptotic distributions of partial sums of functionals of infinite-variance moving averages
    • Hsing T. On the asymptotic distributions of partial sums of functionals of infinite-variance moving averages. Ann. Probab. 27 (1999) 1579-1599
    • (1999) Ann. Probab. , vol.27 , pp. 1579-1599
    • Hsing, T.1
  • 38
    • 0000636504 scopus 로고
    • Some limit theorems for stationary processes
    • Ibragimov I.A. Some limit theorems for stationary processes. Theory Probab. Appl. 7 (1962) 349-382
    • (1962) Theory Probab. Appl. , vol.7 , pp. 349-382
    • Ibragimov, I.A.1
  • 40
    • 36549085102 scopus 로고    scopus 로고
    • Estimating the tail dependence function of an elliptical distribution
    • Klüppleberg C., Kuhn G., and Peng L. Estimating the tail dependence function of an elliptical distribution. Bernoulli 13 (2007) 229-251
    • (2007) Bernoulli , vol.13 , pp. 229-251
    • Klüppleberg, C.1    Kuhn, G.2    Peng, L.3
  • 41
    • 0000583214 scopus 로고
    • Extremes and local dependence in stationary sequences
    • Leadbetter M.R. Extremes and local dependence in stationary sequences. Z. Wahrsch. Verw. Geb 65 (1983) 291-306
    • (1983) Z. Wahrsch. Verw. Geb , vol.65 , pp. 291-306
    • Leadbetter, M.R.1
  • 42
    • 0001470828 scopus 로고
    • On central limit theory for families of strongly mixing additive set functions
    • Cambanis S., and Sen P.K. (Eds), Springer, New York
    • Leadbetter M.R., and Rootzén H. On central limit theory for families of strongly mixing additive set functions. In: Cambanis S., and Sen P.K. (Eds). Festschrift in Honour of Gopinath Kallianpur (1993), Springer, New York 211-223
    • (1993) Festschrift in Honour of Gopinath Kallianpur , pp. 211-223
    • Leadbetter, M.R.1    Rootzén, H.2
  • 44
    • 0001484870 scopus 로고    scopus 로고
    • Modeling dependence within joint tail regions
    • Ledford A.W., and Tawn J.A. Modeling dependence within joint tail regions. J. Roy. Statist. Soc. Ser. B 59 (1997) 475-499
    • (1997) J. Roy. Statist. Soc. Ser. B , vol.59 , pp. 475-499
    • Ledford, A.W.1    Tawn, J.A.2
  • 45
    • 0037769478 scopus 로고    scopus 로고
    • Diagnostics for dependence within time series extremes
    • Ledford A.W., and Tawn J.A. Diagnostics for dependence within time series extremes. J. Roy. Statist. Soc. Ser. B 65 (2003) 521-543
    • (2003) J. Roy. Statist. Soc. Ser. B , vol.65 , pp. 521-543
    • Ledford, A.W.1    Tawn, J.A.2
  • 46
    • 0001411703 scopus 로고
    • A strong invariance theorem for the tail empirical process
    • Mason D. A strong invariance theorem for the tail empirical process. Ann. Inst. H. Poincare 24 (1988) 491-506
    • (1988) Ann. Inst. H. Poincare , vol.24 , pp. 491-506
    • Mason, D.1
  • 47
    • 0000964674 scopus 로고
    • Dependent central limit theorems
    • McLeish D.L. Dependent central limit theorems. Ann. Probab. 2 (1974) 620-628
    • (1974) Ann. Probab. , vol.2 , pp. 620-628
    • McLeish, D.L.1
  • 48
    • 0001915127 scopus 로고
    • A maximal inequality and dependent strong laws
    • McLeish D.L. A maximal inequality and dependent strong laws. Ann. Probab. 3 (1975) 829-839
    • (1975) Ann. Probab. , vol.3 , pp. 829-839
    • McLeish, D.L.1
  • 49
    • 42449162246 scopus 로고    scopus 로고
    • Stability of nonlinear AR-GARCH models
    • Meitz M., and Saikkonen P. Stability of nonlinear AR-GARCH models. J. Time Ser. Anal. 29 (2008) 453-475
    • (2008) J. Time Ser. Anal. , vol.29 , pp. 453-475
    • Meitz, M.1    Saikkonen, P.2
  • 50
    • 0001159892 scopus 로고
    • On weak convergence of stochastic processes with multidimensional time parameter
    • Neuhas G. On weak convergence of stochastic processes with multidimensional time parameter. Ann. Math. Statist. 42 (1971) 1285-1295
    • (1971) Ann. Math. Statist. , vol.42 , pp. 1285-1295
    • Neuhas, G.1
  • 51
    • 84963015112 scopus 로고
    • Multiple time series regression with integrated processes
    • Phillips P.C.B., and Durlauf S.N. Multiple time series regression with integrated processes. Rev. Econom. Stud. 53 (1986) 473-495
    • (1986) Rev. Econom. Stud. , vol.53 , pp. 473-495
    • Phillips, P.C.B.1    Durlauf, S.N.2
  • 52
    • 33747343683 scopus 로고    scopus 로고
    • Central limit theorems for partial sums of bounded functionals of infinite-variance moving averages
    • Pipiras V., and Taqqu M.S. Central limit theorems for partial sums of bounded functionals of infinite-variance moving averages. Bernoulli 9 (2003) 833-855
    • (2003) Bernoulli , vol.9 , pp. 833-855
    • Pipiras, V.1    Taqqu, M.S.2
  • 53
    • 47249094864 scopus 로고    scopus 로고
    • Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation
    • Pipiras V., Taqqu M.S., and Abry P. Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation. Bernoulli 13 (2007) 1091-1123
    • (2007) Bernoulli , vol.13 , pp. 1091-1123
    • Pipiras, V.1    Taqqu, M.S.2    Abry, P.3
  • 55
    • 0039551302 scopus 로고
    • The tail empirical process for stationary sequences
    • Department of Mathematical Statistics, Chalmers University of Technology
    • Rootzén, H., 1995. The tail empirical process for stationary sequences. Report 1995:9, Department of Mathematical Statistics, Chalmers University of Technology.
    • (1995) Report 1995 , vol.9
    • Rootzén, H.1
  • 56
    • 0032222171 scopus 로고    scopus 로고
    • On the distribution of tail array sums for strongly mixing stationary sequences
    • Rootzén H., Leadbetter M., and de Haan L. On the distribution of tail array sums for strongly mixing stationary sequences. Ann. Probab. 8 (1998) 868-885
    • (1998) Ann. Probab. , vol.8 , pp. 868-885
    • Rootzén, H.1    Leadbetter, M.2    de Haan, L.3
  • 57
    • 33745318081 scopus 로고    scopus 로고
    • Non-parametric estimation of tail dependence
    • Schmidt R., and Stadtmüller U. Non-parametric estimation of tail dependence. Scand. J. Statist. 33 (2006) 307-335
    • (2006) Scand. J. Statist. , vol.33 , pp. 307-335
    • Schmidt, R.1    Stadtmüller, U.2
  • 58
    • 0036003757 scopus 로고    scopus 로고
    • The invariance principle for linear processes with applications
    • Wang Q.Y., Lin Y.X., and Gulati C.M. The invariance principle for linear processes with applications. Econometric Theory 18 (2002) 119-139
    • (2002) Econometric Theory , vol.18 , pp. 119-139
    • Wang, Q.Y.1    Lin, Y.X.2    Gulati, C.M.3
  • 59
    • 0001464704 scopus 로고
    • Inequalities with applications to the weak convergence of random processes with multidimensional time parameters
    • Wichura M.J. Inequalities with applications to the weak convergence of random processes with multidimensional time parameters. Ann. Math. Statist. 40 (1969) 681-687
    • (1969) Ann. Math. Statist. , vol.40 , pp. 681-687
    • Wichura, M.J.1
  • 60
    • 84974313169 scopus 로고
    • Some invariance principles and central limit theorems for dependent heterogeneous processes
    • Wooldridge J.M., and White H. Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometric Theory 4 (1988) 210-230
    • (1988) Econometric Theory , vol.4 , pp. 210-230
    • Wooldridge, J.M.1    White, H.2
  • 61
    • 17844387350 scopus 로고    scopus 로고
    • On linear processes with dependent innovations
    • Wu W.B., and Min M. On linear processes with dependent innovations. Stochastic Process. Appl. 115 (2005) 939-958
    • (2005) Stochastic Process. Appl. , vol.115 , pp. 939-958
    • Wu, W.B.1    Min, M.2
  • 62
    • 3042646584 scopus 로고    scopus 로고
    • Martingale approximations for sums of stationary processes
    • Wu W.B., and Woodroofe M. Martingale approximations for sums of stationary processes. Ann. Probab. 32 (2004) 1674-1690
    • (2004) Ann. Probab. , vol.32 , pp. 1674-1690
    • Wu, W.B.1    Woodroofe, M.2


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