메뉴 건너뛰기




Volumn 80, Issue 1, 1999, Pages 15-35

Convergence of normalized quadratic forms

Author keywords

Appell polynomials; Long range dependence; Non central limit theorem; Quadratic forms; Time series

Indexed keywords


EID: 0033176760     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(98)00240-7     Document Type: Article
Times cited : (12)

References (28)
  • 1
    • 0009040435 scopus 로고
    • Central limit theorems for sums of Wick products of stationary sequences
    • Avram, F., Fox, R., 1992. Central limit theorems for sums of Wick products of stationary sequences. Trans. Amer. Math. Soc. 330 (2), 651-663.
    • (1992) Trans. Amer. Math. Soc. , vol.330 , Issue.2 , pp. 651-663
    • Avram, F.1    Fox, R.2
  • 2
    • 0000829711 scopus 로고
    • Noncentral limit theorems and Appell polynomials
    • Avram, F., Taqqu, M.S., 1987. Noncentral limit theorems and Appell polynomials. Ann. Probab. 15, 767-775.
    • (1987) Ann. Probab. , vol.15 , pp. 767-775
    • Avram, F.1    Taqqu, M.S.2
  • 4
    • 0000323474 scopus 로고
    • Central limit theorems for non-linear functionals of Gaussian fields
    • Breuer, P., Major, P., 1983. Central limit theorems for non-linear functionals of Gaussian fields. J. Multivariate Anal. 13, 425-441.
    • (1983) J. Multivariate Anal. , vol.13 , pp. 425-441
    • Breuer, P.1    Major, P.2
  • 5
    • 0001627705 scopus 로고
    • The empirical process of some long-range dependent sequences with an application to U-statistics
    • Dehling, H., Taqqu, M.S., 1989. The empirical process of some long-range dependent sequences with an application to U-statistics. Ann. Statist. 17, 1767-1783.
    • (1989) Ann. Statist. , vol.17 , pp. 1767-1783
    • Dehling, H.1    Taqqu, M.S.2
  • 7
    • 0002188727 scopus 로고
    • Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series
    • Fox, R., Taqqu, M.S., 1986. Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14, 517-532.
    • (1986) Ann. Statist. , vol.14 , pp. 517-532
    • Fox, R.1    Taqqu, M.S.2
  • 8
    • 0001340698 scopus 로고
    • Central limit theorems for quadratic forms in random variables having long-range dependence
    • Fox, R., Taqqu, M.S., 1987. Central limit theorems for quadratic forms in random variables having long-range dependence. Probab. Theory Related Fields 74, 213-240.
    • (1987) Probab. Theory Related Fields , vol.74 , pp. 213-240
    • Fox, R.1    Taqqu, M.S.2
  • 9
    • 0002646404 scopus 로고
    • Central limit theorem for functionals of a linear process
    • Giraitis, L., 1985. Central limit theorem for functionals of a linear process. Lithuanian Math. J. 25, 25-35.
    • (1985) Lithuanian Math. J. , vol.25 , pp. 25-35
    • Giraitis, L.1
  • 10
    • 51249172022 scopus 로고
    • CLT and other limit theorems for functionals of Gaussian processes
    • Giraitis, L., Surgailis, D., 1985. CLT and other limit theorems for functionals of Gaussian processes. Probab. Theory Related Fields 70, 191-212.
    • (1985) Probab. Theory Related Fields , vol.70 , pp. 191-212
    • Giraitis, L.1    Surgailis, D.2
  • 11
    • 0001865584 scopus 로고
    • Multivariate Appell polynomials and the central limit theorem
    • Eberlein, E., Taqqu, M.S. (Eds.), Birkhäuser, New York
    • Giraitis, L., Surgailis, D., 1986. Multivariate Appell polynomials and the central limit theorem. In: Eberlein, E., Taqqu, M.S. (Eds.), Dependence in Probability and Statistics. Birkhäuser, New York, pp. 21-71.
    • (1986) Dependence in Probability and Statistics , pp. 21-71
    • Giraitis, L.1    Surgailis, D.2
  • 12
    • 0001551839 scopus 로고
    • Limit theorem for polynomials of linear processes with long range dependence
    • Giraitis, L., Surgailis, D., 1989. Limit theorem for polynomials of linear processes with long range dependence. Lietuvos Matematikos Rinkinys 29, 128-145.
    • (1989) Lietuvos Matematikos Rinkinys , vol.29 , pp. 128-145
    • Giraitis, L.1    Surgailis, D.2
  • 13
    • 0001898682 scopus 로고
    • A central limit theorem for quadratic forms in strongly dependent linear variables and application to asymptotical normality of Whittle's estimate
    • Giraitis, L., Surgailis, D., 1990. A central limit theorem for quadratic forms in strongly dependent linear variables and application to asymptotical normality of Whittle's estimate. Probab. Theory Related Fields 86, 87-104.
    • (1990) Probab. Theory Related Fields , vol.86 , pp. 87-104
    • Giraitis, L.1    Surgailis, D.2
  • 14
    • 0008985697 scopus 로고
    • A central limit theorem for the empirical process of a long memory linear sequence
    • Universität Heidelberg
    • Giraitis, L., Surgailis, D., 1994. A central limit theorem for the empirical process of a long memory linear sequence. Beiträge für Statistik, Universität Heidelberg, http://statlab.uni-heidelberg.de/rports/www.html 24, 1-13.
    • (1994) Beiträge für Statistik , vol.24 , pp. 1-13
    • Giraitis, L.1    Surgailis, D.2
  • 16
    • 0009066808 scopus 로고    scopus 로고
    • Central limit theorems for quadratic forms with time-domain conditions
    • to appear
    • Giraitis, L., Taqqu, M.S., 1997a. Central limit theorems for quadratic forms with time-domain conditions. Ann. Probab., to appear.
    • (1997) Ann. Probab.
    • Giraitis, L.1    Taqqu, M.S.2
  • 17
    • 0031487197 scopus 로고    scopus 로고
    • Limit theorems for bivariate Appell polynomials: Part I. Central limit theorems
    • Giraitis, L., Taqqu, M.S., 1997b. Limit theorems for bivariate Appell polynomials: Part I. Central limit theorems. Probab. Theory Related Fields 107, 359-381.
    • (1997) Probab. Theory Related Fields , vol.107 , pp. 359-381
    • Giraitis, L.1    Taqqu, M.S.2
  • 18
    • 85045586223 scopus 로고    scopus 로고
    • Limit theorems for bivariate Appell polynomials: Part II. Non-central limit theorems
    • to appear
    • Giraitis, L., Taqqu, M.S., Terrin, N., 1997. Limit theorems for bivariate Appell polynomials: Part II. Non-central limit theorems. Probab. Theory Related Fields, to appear.
    • (1997) Probab. Theory Related Fields
    • Giraitis, L.1    Taqqu, M.S.2    Terrin, N.3
  • 19
    • 84986792205 scopus 로고
    • An introduction to long-memory time series and fractional differencing
    • Granger, C.W.J., Joyeux, R., 1980. An introduction to long-memory time series and fractional differencing. J. Time Ser. Anal. 1, 15-30.
    • (1980) J. Time Ser. Anal. , vol.1 , pp. 15-30
    • Granger, C.W.J.1    Joyeux, R.2
  • 20
    • 0030500327 scopus 로고    scopus 로고
    • On the asymptotic expansion of the empirical process of long memory moving averages
    • Ho, H.C., Hsing, T., 1996. On the asymptotic expansion of the empirical process of long memory moving averages. Ann. Statist. 24, 992-1024.
    • (1996) Ann. Statist. , vol.24 , pp. 992-1024
    • Ho, H.C.1    Hsing, T.2
  • 21
    • 77956890381 scopus 로고
    • Fractional differencing
    • Hosking, J.R.M., 1981. Fractional differencing. Biometrika 68 (1), 165-176.
    • (1981) Biometrika , vol.68 , Issue.1 , pp. 165-176
    • Hosking, J.R.M.1
  • 22
    • 0031518524 scopus 로고    scopus 로고
    • Asymptotic expansion of M-estimators with long memory errors
    • Koul, H.L., Surgailis, D., 1997. Asymptotic expansion of M-estimators with long memory errors. Ann. Statist. 25, 818-850.
    • (1997) Ann. Statist. , vol.25 , pp. 818-850
    • Koul, H.L.1    Surgailis, D.2
  • 23
    • 0000501589 scopus 로고
    • Fractional Brownian motions, fractional noises and applications
    • Mandelbrot, B.B., Van Ness, J.W., 1968. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422-437.
    • (1968) SIAM Rev. , vol.10 , pp. 422-437
    • Mandelbrot, B.B.1    Van Ness, J.W.2
  • 25
    • 0000297429 scopus 로고
    • Zones of attraction of self-similar multiple integrals
    • Surgailis, D., 1982. Zones of attraction of self-similar multiple integrals. Lithuanian Math. J. 22, 327-340.
    • (1982) Lithuanian Math. J. , vol.22 , pp. 327-340
    • Surgailis, D.1
  • 26
    • 34250409798 scopus 로고
    • Weak convergence to fractional Brownian motion and to the Rosenblatt process
    • Taqqu, M.S., 1975. Weak convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheorie und verwandte Gebiete 31, 287-302.
    • (1975) Z. Wahrscheinlichkeitstheorie und Verwandte Gebiete , vol.31 , pp. 287-302
    • Taqqu, M.S.1
  • 27
    • 0000593269 scopus 로고
    • A noncentral limit theorem for quadratic forms of Gaussian stationary sequences
    • Terrin, N., Taqqu, M.S., 1990. A noncentral limit theorem for quadratic forms of Gaussian stationary sequences. J. Theoret. Probab. 3, 449-475.
    • (1990) J. Theoret. Probab. , vol.3 , pp. 449-475
    • Terrin, N.1    Taqqu, M.S.2
  • 28
    • 0009075739 scopus 로고
    • Convergence in distribution of sums of bivariate Appell polynomials with long-range dependence
    • Terrin, N., Taqqu, M.S., 1991. Convergence in distribution of sums of bivariate Appell polynomials with long-range dependence. Probab. Theory Related Fields 90, 57-81.
    • (1991) Probab. Theory Related Fields , vol.90 , pp. 57-81
    • Terrin, N.1    Taqqu, M.S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.