메뉴 건너뛰기




Volumn 40, Issue 5, 2012, Pages 2008-2033

A functional limit theorem for dependent sequences with infinite variance stable limits

Author keywords

Convergence in distribution; functional limit theorem; GARCH; Mixing; oving average; Partial sum; Point processes; Regular variation; Spectral processes; Stable processes; Tochastic volatility

Indexed keywords


EID: 84872580081     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOP669     Document Type: Article
Times cited : (67)

References (49)
  • 1
    • 41449118528 scopus 로고    scopus 로고
    • Selection from a stable box
    • MR2401656
    • AUE, A., BERKES, I. and HORVÁTH, L. (2008). Selection from a stable box. Bernoulli 14 125-139. MR2401656
    • (2008) Bernoulli , vol.14 , pp. 125-139
    • Aue, A.1    Berkes, I.2    Horváth, L.3
  • 2
    • 0001643692 scopus 로고
    • Weak convergence of sums of moving averages in the α-stable domain of attraction
    • MR1143432
    • AVRAM, F. and TAQQU, M. S. (1992). Weak convergence of sums of moving averages in the α-stable domain of attraction. Ann. Probab. 20 483-503. MR1143432
    • (1992) Ann. Probab. , vol.20 , pp. 483-503
    • Avram, F.1    Taqqu, M.S.2
  • 5
    • 61849184868 scopus 로고    scopus 로고
    • Regularly varying multivariate time series
    • MR2508565
    • BASRAK, B. and SEGERS, J. (2009). Regularly varying multivariate time series. Stochastic Process. Appl. 119 1055-1080. MR2508565
    • (2009) Stochastic Process. Appl. , vol.11
    • Basrak, B.1    Segers, J.2
  • 6
    • 4043059348 scopus 로고    scopus 로고
    • Lévy Processes
    • Cambridge Univ. Press, Cambridge. MR1406564
    • BERTOIN, J. (1996). Lévy Processes. Cambridge Tracts in Math. 121. Cambridge Univ. Press, Cambridge. MR1406564
    • (1996) Cambridge Tracts in Math , vol.121
    • Bertoin, J.1
  • 7
    • 0003407041 scopus 로고
    • Convergence of Probability Measures
    • New York.
    • BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.MR0233396
    • (1968) Wiley
    • Billingsley, P.1
  • 8
    • 0007192502 scopus 로고
    • Time Series: Theory and Methods, 2nd ed
    • New York. MR1093459
    • BROCKWELL, P. J. and DAVIS, R. A. (1991). Time Series: Theory and Methods, 2nd ed.Springer, New York. MR1093459
    • (1991) Springer
    • Brockwell, P.J.1    Davis, R.A.2
  • 9
    • 0001830785 scopus 로고
    • Stable limits for associated random variables
    • MR1258863
    • DABROWSKI, A. R. and JAKUBOWSKI, A. (1994). Stable limits for associated random variables.Ann. Probab. 22 1-16. MR1258863
    • (1994) Ann. Probab. , vol.22 , pp. 1-16
    • Dabrowski, A.R.1    Jakubowski, A.2
  • 10
    • 0001568756 scopus 로고
    • Limit theory for moving averages of random variables with regularly varying tail probabilities
    • MR0770636
    • DAVIS, R. and RESNICK, S. (1985). Limit theory for moving averages of random variables with regularly varying tail probabilities. Ann. Probab. 13 179-195. MR0770636
    • (1985) Ann. Probab. , vol.13 , pp. 179-195
    • Davis, R.1    Resnick, S.2
  • 11
    • 0011020531 scopus 로고
    • Stable limits for partial sums of dependent random variables
    • MR0690127
    • DAVIS, R. A. (1983). Stable limits for partial sums of dependent random variables. Ann.Probab. 11 262-269. MR0690127
    • (1983) Ann.Probab. , vol.11 , pp. 262-269
    • Davis, R.A.1
  • 12
    • 0001094957 scopus 로고
    • Point process and partial sum convergence for weakly dependent random variables with infinite variance
    • MR1334176
    • DAVIS, R. A. and HSING, T. (1995). Point process and partial sum convergence for weakly dependent random variables with infinite variance. Ann. Probab. 23 879-917. MR1334176
    • (1995) Ann. Probab. , vol.23 , pp. 879-917
    • Davis, R.A.1    Mikosch, T.2
  • 13
    • 0032264526 scopus 로고    scopus 로고
    • The sample autocorrelations of heavy-tailed processes with applications to ARCH
    • MR1673289
    • DAVIS, R. A. and MIKOSCH, T. (1998). The sample autocorrelations of heavy-tailed processes with applications to ARCH. Ann. Statist. 26 2049-2080. MR1673289
    • (1998) Ann. Statist. , vol.26 , pp. 2049-2080
    • Davis, R.A.1    Mikosch, T.2
  • 14
    • 77649229701 scopus 로고    scopus 로고
    • The extremogram: A correlogram for extreme events
    • MR2597580
    • DAVIS, R. A. and MIKOSCH, T. (2009). The extremogram: A correlogram for extreme events. Bernoulli 15 977-1009. MR2597580
    • (2009) Bernoulli , vol.15 , pp. 977-1009
    • Davis, R.A.1    Mikosch, T.2
  • 16
    • 38249005646 scopus 로고
    • Stable limit distributions for strongly mixing sequences
    • MR1040810
    • DENKER, M. and JAKUBOWSKI, A. (1989). Stable limit distributions for strongly mixing sequences. Statist. Probab. Lett. 8 477-483. MR1040810
    • (1989) Statist. Probab. Lett. , vol.8 , pp. 477-483
    • Denker, M.1    Jakubowski, A.2
  • 17
    • 0000918549 scopus 로고
    • Functional limit theorems for dependent variables
    • MR0503954
    • DURRETT, R. and RESNICK, S. I. (1978). Functional limit theorems for dependent variables. Ann. Probab. 6 829-846. MR0503954
    • (1978) Ann. Probab. , vol.6 , pp. 829-846
    • Durrett, R.1    Resnick, S.I.2
  • 19
    • 0003421261 scopus 로고
    • An Introduction to Probability Theory and Its Applications
    • Wiley, New York. MR0270403
    • FELLER, W. (1971). An Introduction to Probability Theory and Its Applications. Vol. II, 2nd ed. Wiley, New York. MR0270403
    • (1971) Vol. II, 2nd ed.
    • Feller, W.1
  • 20
    • 0003513648 scopus 로고
    • Limit Distributions for Sums of Independent Random Variables
    • Cambridge, MA. MR0062975
    • GNEDENKO, B. V. and KOLMOGOROV, A. N. (1954). Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Cambridge, MA. MR0062975
    • (1954) Addison-Wesley
    • Gnedenko, B.V.1    Kolmogorov, A.N.2
  • 21
    • 0000732230 scopus 로고
    • Implicit renewal theory and tails of solutions of random equations
    • MR1097468
    • GOLDIE, C. M. (1991). Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1 126-166. MR1097468
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 126-166
    • Goldie, C.M.1
  • 22
    • 10744227440 scopus 로고    scopus 로고
    • Central limit theorem and stable laws for intermittent maps
    • MR2027296
    • GOUËZEL, S. (2004). Central limit theorem and stable laws for intermittent maps. Probab. Theory Related Fields 128 82-122. MR2027296
    • (2004) Probab. Theory Related Fields , vol.128 , pp. 82-122
    • Gouëzel, S.1
  • 23
    • 0002158552 scopus 로고
    • A functional central limit theorem for strongly mixing sequences of random variables
    • MR0791910
    • HERRNDORF, N. (1985). A functional central limit theorem for strongly mixing sequences of random variables. Z. Wahrsch. Verw. Gebiete 69 541-550. MR0791910
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.69 , pp. 541-550
    • Herrndorf, N.1
  • 24
    • 38249005991 scopus 로고
    • Minimal conditions in p-stable limit theorems
    • MR1200412
    • JAKUBOWSKI, A. (1993). Minimal conditions in p-stable limit theorems. Stochastic Process. Appl. 44 291-327. MR1200412
    • (1993) Stochastic Process. Appl. , vol.44 , pp. 291-327
    • Jakubowski, A.1
  • 25
    • 0031591380 scopus 로고    scopus 로고
    • Minimal conditions in p-stable limit theorems
    • MR1454576
    • JAKUBOWSKI, A. (1997). Minimal conditions in p-stable limit theorems. II. Stochastic Process. Appl. 68 1-20. MR1454576
    • (1997) II. Stochastic Process. Appl. , vol.68 , pp. 1-20
    • Jakubowski, A.1
  • 26
    • 0010985291 scopus 로고
    • A-stable limit theorems for sums of dependent random vectors
    • MR1004336
    • JAKUBOWSKI, A. and KOBUS, M. (1989). a-stable limit theorems for sums of dependent random vectors. J. Multivariate Anal. 29 219-251. MR1004336
    • (1989) J. Multivariate Anal. , vol.29 , pp. 219-251
    • Jakubowski, A.1    Kobus, M.2
  • 27
    • 85043048186 scopus 로고
    • Random Measures, 3rd ed
    • Berlin. MR0818219
    • KALLENBERG, O. (1983). Random Measures, 3rd ed. Akademie-Verlag, Berlin. MR0818219
    • (1983) Akademie-Verlag
    • Kallenberg, O.1
  • 28
    • 0004201402 scopus 로고    scopus 로고
    • Foundations of Modern Probability
    • New York. MR1464694
    • KALLENBERG, O. (1997). Foundations of Modern Probability. Springer, New York. MR1464694
    • (1997) Springer
    • Kallenberg, O.1
  • 29
    • 0000803498 scopus 로고
    • On strong mixing conditions for stationary Gaussian process
    • KOLMOGOROV, A. N. and ROZANOV, Y. A. (1960). On strong mixing conditions for stationary Gaussian process. Theory Probab. Appl. 5 204-208.
    • (1960) Theory Probab. Appl. , vol.5 , pp. 204-208
    • Kolmogorov, A.N.1    Rozanov, Y.A.2
  • 30
    • 84872520152 scopus 로고    scopus 로고
    • Functional limit theorems for weakly dependent regularly varying time series
    • Available at
    • KRIZMANÍC, D. (2010). Functional limit theorems for weakly dependent regularly varying time series. Ph.D. thesis, Univ. Zagreb. Available at http://www.math.uniri.hr/dkrizmanic/DKthesis.pdf.
    • (2010) Ph.D. thesis, Univ. Zagreb
    • Krizmaníc, D.1
  • 31
    • 0001433650 scopus 로고
    • Extremal theory for stochastic processes
    • MR0929071
    • LEADBETTER, M. R. and ROOTZÉN, H. (1988). Extremal theory for stochastic processes. Ann. Probab. 16 431-478. MR0929071
    • (1988) Ann. Probab. , vol.16 , pp. 431-478
    • Leadbetter, M.R.1    Rootzén, H.2
  • 32
    • 0000994389 scopus 로고
    • Convergence to a stable distribution via order statistics
    • MR0624688
    • LEPAGE, R., WOODROOFE, M. and ZINN, J. (1981). Convergence to a stable distribution via order statistics. Ann. Probab. 9 624-632. MR0624688
    • (1981) Ann. Probab. , vol.9 , pp. 624-632
    • Lepage, R.1    Woodroofe, M.2    Zinn, J.3
  • 34
    • 0034214586 scopus 로고    scopus 로고
    • The functional central limit theorem under the strong mixing condition
    • MR1797876
    • MERLEVÉDE, F. and PELIGRAD, M. (2000). The functional central limit theorem under the strong mixing condition. Ann. Probab. 28 1336-1352. MR1797876
    • (2000) Ann. Probab. , vol.28 , pp. 1336-1352
    • Merlevéde, F.1    Peligrad, M.2
  • 35
    • 0034287159 scopus 로고    scopus 로고
    • Limit theory for the sample autocorrelations and extremes of a GARCH (1, 1) process
    • MR1805791
    • MIKOSCH, T. and STǎRICǎ, C. (2000). Limit theory for the sample autocorrelations and extremes of a GARCH (1, 1) process. Ann. Statist. 28 1427-1451. MR1805791
    • (2000) Ann. Statist. , vol.28 , pp. 1427-1451
    • Mikosch, T.1    Stǎricǎ, C.2
  • 36
    • 0002047692 scopus 로고
    • Limit distributions of two-dimensional point processes generated by strongmixing sequences
    • MR0467887
    • MORI, T. (1977). Limit distributions of two-dimensional point processes generated by strongmixing sequences. Yokohama Math. J. 25 155-168. MR0467887
    • (1977) Yokohama Math. J. , vol.25 , pp. 155-168
    • Mori, T.1
  • 37
    • 17044387009 scopus 로고    scopus 로고
    • A new maximal inequality and invariance principle for stationary sequences
    • MR2123210
    • PELIGRAD, M. and UTEV, S. (2005). A new maximal inequality and invariance principle for stationary sequences. Ann. Probab. 33 798-815. MR2123210
    • (2005) Ann. Probab. , vol.33 , pp. 798-815
    • Peligrad, M.1    Utev, S.2
  • 38
    • 0039893700 scopus 로고
    • Limit Theorems of Probability Theory: Sequences of Independent Random Variables
    • Clarendon, Oxford Univ. Press, New York. MR1353441
    • PETROV, V. V. (1995). Limit Theorems of Probability Theory: Sequences of Independent Random Variables. Oxford Studies in Probability 4. Clarendon, Oxford Univ. Press, New York. MR1353441
    • (1995) Oxford Studies in Probability , vol.4
    • Petrov, V.V.1
  • 39
    • 0001155464 scopus 로고
    • Some mixing properties of time series models
    • MR0787587
    • PHAM, T. D. and TRAN, L. T. (1985). Some mixing properties of time series models. Stochastic Process. Appl. 19 297-303. MR0787587
    • (1985) Stochastic Process. Appl. , vol.19 , pp. 297-303
    • Pham, T.D.1    Tran, L.T.2
  • 40
    • 0002095272 scopus 로고
    • Point processes, regular variation and weak convergence
    • MR0827332
    • RESNICK, S. I. (1986). Point processes, regular variation and weak convergence. Adv. in Appl. Probab. 18 66-138. MR0827332
    • (1986) Adv. in Appl. Probab. , vol.18 , pp. 66-138
    • Resnick, S.I.1
  • 41
    • 85046584195 scopus 로고    scopus 로고
    • Heavy-Tail Phenomena: Probabilistic and Statistical Modeling
    • New York. MR2271424
    • RESNICK, S. I. (2007). Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. Springer, New York. MR2271424
    • (2007) Springer
    • Resnick, S.I.1
  • 42
    • 0003232762 scopus 로고    scopus 로고
    • Lévy Processes and Infinitely Divisible Distributions
    • Cambridge Univ. Press, Cambridge. MR1739520
    • SATO, K.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge Stud. Adv. Math. 68. Cambridge Univ. Press, Cambridge. MR1739520
    • (1999) Cambridge Stud. Adv. Math. , vol.68
    • Sato, K.-I.1
  • 43
    • 0344082898 scopus 로고    scopus 로고
    • Functionals of clusters of extremes
    • MR2014268
    • SEGERS, J. (2003). Functionals of clusters of extremes. Adv. in Appl. Probab. 35 1028-1045. MR2014268
    • (2003) Adv. in Appl. Probab. , vol.35 , pp. 1028-1045
    • Segers, J.1
  • 44
    • 25144469282 scopus 로고    scopus 로고
    • Approximate distributions of clusters of extremes
    • MR2186477
    • SEGERS, J. (2005). Approximate distributions of clusters of extremes. Statist. Probab. Lett. 74 330-336. MR2186477
    • (2005) Statist. Probab. Lett. , vol.74 , pp. 330-336
    • Segers, J.1
  • 45
    • 0000683243 scopus 로고
    • Limit theorems for stochastic processes with independent increments
    • MR0094842
    • SKOROHOD, A. V. (1957). Limit theorems for stochastic processes with independent increments. Theory Probab. Appl. 2 145-177. MR0094842
    • (1957) Theory Probab. Appl. , vol.2 , pp. 145-177
    • Skorohod, A.V.1
  • 46
    • 51949093459 scopus 로고    scopus 로고
    • Nonstandard limit theorem for infinite variance functionals
    • MR2393998
    • SLY, A. and HEYDE, C. (2008). Nonstandard limit theorem for infinite variance functionals. Ann. Probab. 36 796-805. MR2393998
    • (2008) Ann. Probab. , vol.36 , pp. 796-805
    • Szl, A.1    Heyde, C.2
  • 47
    • 0001782542 scopus 로고
    • The extremal index for a Markov chain
    • MR1147765
    • SMITH, R. L. (1992). The extremal index for a Markov chain. J. Appl. Probab. 29 37-45. MR1147765
    • (1992) J. Appl. Probab , vol.29 , pp. 37-45
    • Smith, R.L.1
  • 48
    • 77955418389 scopus 로고    scopus 로고
    • Convergence to Lévy stable processes under some weak dependence conditions
    • MR2673968
    • TYRAN-KAMIŃ SKA, M. (2010). Convergence to Lévy stable processes under some weak dependence conditions. Stochastic Process. Appl. 120 1629-1650. MR2673968
    • (2010) Stochastic Process. Appl. , vol.120 , pp. 1629-1650
    • Tyran-Kamińska, M.1
  • 49
    • 77952239320 scopus 로고    scopus 로고
    • Functional limit theorems for linear processes in the domain of attraction of stable laws
    • MR2638967
    • TYRAN-KAMIŃ SKA, M. (2010). Functional limit theorems for linear processes in the domain of attraction of stable laws. Statist. Probab. Lett. 80 975-981. MR2638967
    • (2010) Statist. Probab. Lett. , vol.80 , pp. 975-981
    • Tyran-Kamińska, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.