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Volumn 26, Issue 2, 2005, Pages 211-249

Asymptotic self-similarity and wavelet estimation for long-range dependent fractional autoregressive integrated moving average time series with stable innovations

Author keywords

Asymptotic normality; Fractional autoregressive integrated moving average; Fractional difference parameter estimators; Linear fractional stable motion; Long range dependence; Mallat's algorithm; Symmetric stable; Wavelets

Indexed keywords


EID: 14644415873     PISSN: 01439782     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1467-9892.2005.00399.x     Document Type: Article
Times cited : (31)

References (37)
  • 1
    • 0031700563 scopus 로고    scopus 로고
    • Wavelet analysis of long range dependent traffic
    • ABRY, P. and VEITCH, D. (1998) Wavelet analysis of long range dependent traffic. IEEE Transactions on Information Theory 44(1), 2-15.
    • (1998) IEEE Transactions on Information Theory , vol.44 , Issue.1 , pp. 2-15
    • Abry, P.1    Veitch, D.2
  • 3
    • 0010979117 scopus 로고    scopus 로고
    • Estimation ondelette, des paramètres de stabilité et d'autosimilarité des processus α-stables autosimilaires
    • Vannes (September 13-17, 1999). Organized by IRCYN-IRISA-ERNST Bretagne
    • ABRY, P., PESQUET-POPESCU, B. and TAQQU, M. S. (2000) Estimation ondelette, des paramètres de stabilité et d'autosimilarité des processus α-stables autosimilaires. In Proceedings of the 17th GRETSI Symposium on Signal and Image Processing Vol. 4, Vannes (September 13-17, 1999). Organized by IRCYN-IRISA-ERNST Bretagne, pp. 933-6.
    • (2000) Proceedings of the 17th GRETSI Symposium on Signal and Image Processing , vol.4 , pp. 933-936
    • Abry, P.1    Pesquet-Popescu, B.2    Taqqu, M.S.3
  • 4
    • 14644410506 scopus 로고    scopus 로고
    • Self-similarity and long-range dependence through the wavelet lens
    • (eds P. DOUKHAN, G. OPPENHEIM and M. S. TAQQU). Birkhäuser
    • ABRY, P., FLANDRIN, P., TAQQU, M. S. and VEITCH, D. (2003) Self-similarity and long-range dependence through the wavelet lens. In Theory and Applications of Long-range Dependence (eds P. DOUKHAN, G. OPPENHEIM and M. S. TAQQU). Birkhäuser, pp. 527-56.
    • (2003) Theory and Applications of Long-range Dependence , pp. 527-556
    • Abry, P.1    Flandrin, P.2    Taqqu, M.S.3    Veitch, D.4
  • 5
    • 0003220909 scopus 로고
    • Limit theorems for sums of linearly generated random variables
    • ASTRAUSKAS, A. (1983) Limit theorems for sums of linearly generated random variables. Lithuanian Mathematical Journal 23(2), 127-34.
    • (1983) Lithuanian Mathematical Journal , vol.23 , Issue.2 , pp. 127-134
    • Astrauskas, A.1
  • 6
    • 0002587835 scopus 로고
    • Weak convergence of moving averages with infinite variance
    • (eds E. EBERLEIN and M. S. TAQQU). Boston: Birkhäuser
    • AVRAM, F. and TAQQU, M. S. (1986) Weak convergence of moving averages with infinite variance. Dependence in Probability and Statistics (eds E. EBERLEIN and M. S. TAQQU). Boston: Birkhäuser, pp. 399-415.
    • (1986) Dependence in Probability and Statistics , pp. 399-415
    • Avram, F.1    Taqqu, M.S.2
  • 7
    • 0000625581 scopus 로고    scopus 로고
    • Testing for the presence of self-similarity of Gaussian time series having stationary increments
    • BARDET, J.-M. (2000) Testing for the presence of self-similarity of Gaussian time series having stationary increments. Journal of Time Series Analysis 21, 497-515.
    • (2000) Journal of Time Series Analysis , vol.21 , pp. 497-515
    • Bardet, J.-M.1
  • 13
  • 14
    • 0001445295 scopus 로고    scopus 로고
    • Stochastic integral representation and properties of the wavelet coefficients of the linear fractional stable motion
    • DELBEKE, L. and ABRY, P. (2000) Stochastic integral representation and properties of the wavelet coefficients of the linear fractional stable motion. Stochastic Processes and their Applications 86, 177-82.
    • (2000) Stochastic Processes and Their Applications , vol.86 , pp. 177-182
    • Delbeke, L.1    Abry, P.2
  • 15
    • 0002188727 scopus 로고
    • Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series
    • Fox, R. and TAQQU, M. S. (1986) Large-sample properties of parameter estimates for strongly dependent stationary Gaussian time series. The Annals of Statistics 14, 517-32.
    • (1986) The Annals of Statistics , vol.14 , pp. 517-532
    • Fox, R.1    Taqqu, M.S.2
  • 16
    • 84986792205 scopus 로고
    • An introduction to long-memory time series and fractional differencing
    • GRANGER, C. W. J. and JOYEUX, R. (1980) An introduction to long-memory time series and fractional differencing. Journal of Time Series Analysis 1, 15-30.
    • (1980) Journal of Time Series Analysis , vol.1 , pp. 15-30
    • Granger, C.W.J.1    Joyeux, R.2
  • 17
    • 77956890381 scopus 로고
    • Fractional differencing
    • HOSKING, J. R. M. (1981) Fractional differencing. Biometrika 68(1), 165-76.
    • (1981) Biometrika , vol.68 , Issue.1 , pp. 165-176
    • Hosking, J.R.M.1
  • 18
    • 0002670989 scopus 로고    scopus 로고
    • The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long memory time series
    • HURVICH, C., DEO, R. and BRODSKY, J. (1998) The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long memory time series. Journal of Time Series Analysis 19, 19-46.
    • (1998) Journal of Time Series Analysis , vol.19 , pp. 19-46
    • Hurvich, C.1    Deo, R.2    Brodsky, J.3
  • 20
    • 0001929163 scopus 로고    scopus 로고
    • Infinite variance stable moving averages with long memory
    • KOKOSZKA, P. S. and TAQQU, M. S. (1996a) Infinite variance stable moving averages with long memory. Journal of Econometrics 73, 79-99.
    • (1996) Journal of Econometrics , vol.73 , pp. 79-99
    • Kokoszka, P.S.1    Taqqu, M.S.2
  • 21
    • 0030359440 scopus 로고    scopus 로고
    • Parameter estimation for infinite variance fractional ARIMA
    • KOKOSZKA, P. S. and TAQQU, M. S. (1996b) Parameter estimation for infinite variance fractional ARIMA. The Annals of Statistics 24, 1880-913.
    • (1996) The Annals of Statistics , vol.24 , pp. 1880-1913
    • Kokoszka, P.S.1    Taqqu, M.S.2
  • 24
    • 0002906495 scopus 로고    scopus 로고
    • Stable Paretian modeling in finance: Some empirical and theoretical aspects
    • (eds R. ADLER, R. FELDMAN and M. S. TAQQU). Boston: Birkhäuser
    • MITTNIK, S., RACHEV, S. T. and PAOLELLA, M. S. (1998) Stable Paretian modeling in finance: some empirical and theoretical aspects. In A Practical Guide to Heavy Tails: Statistical Techniques and Applications (eds R. ADLER, R. FELDMAN and M. S. TAQQU). Boston: Birkhäuser, pp. 79-110.
    • (1998) A Practical Guide to Heavy Tails: Statistical Techniques and Applications , pp. 79-110
    • Mittnik, S.1    Rachev, S.T.2    Paolella, M.S.3
  • 25
    • 0033236911 scopus 로고    scopus 로고
    • Broadband log-periodogram regression of time series with long-range dependence
    • MOULINES, E. and SOULIER, P. (1999) Broadband log-periodogram regression of time series with long-range dependence. The Annals of Statistics 27(4), 1415-39.
    • (1999) The Annals of Statistics , vol.27 , Issue.4 , pp. 1415-1439
    • Moulines, E.1    Soulier, P.2
  • 27
    • 85013350011 scopus 로고
    • Wide-area traffic: The failure of Poisson modeling
    • London, UK
    • PAXON, V. and FLOYD, S. (1994) Wide-area traffic: the failure of Poisson modeling. In Proceedings of the ACM Sigcomm'94. London, UK, pp. 257-68.
    • (1994) Proceedings of the ACM Sigcomm'94 , pp. 257-268
    • Paxon, V.1    Floyd, S.2
  • 29
    • 21344460304 scopus 로고
    • Gaussian semiparametric estimation of long range dependence
    • ROBINSON, P. M. (1995a) Gaussian semiparametric estimation of long range dependence. The Annals of Statistics 23, 1630-61.
    • (1995) The Annals of Statistics , vol.23 , pp. 1630-1661
    • Robinson, P.M.1
  • 30
    • 0000668540 scopus 로고
    • Log-periodogram regression of time series with long range dependence
    • ROBINSON, P. M. (1995b) Log-periodogram regression of time series with long range dependence. The Annals of Statistics 23, 1048-72.
    • (1995) The Annals of Statistics , vol.23 , pp. 1048-1072
    • Robinson, P.M.1
  • 32
    • 0036887887 scopus 로고    scopus 로고
    • Estimation of the self-similarity parameter in linear fractional stable motion
    • STOEV, S., PIPIRAS, V. and TAQQU, M. S. (2002) Estimation of the self-similarity parameter in linear fractional stable motion. Signal Processing 82, 1873-901.
    • (2002) Signal Processing , vol.82 , pp. 1873-1901
    • Stoev, S.1    Pipiras, V.2    Taqqu, M.S.3
  • 33
    • 0009603101 scopus 로고    scopus 로고
    • Semi-parametric graphical estimation techniques for long-memory data
    • Athens Conference on Applied Probability and Time Series Analysis Vol. II: Time Series Analysis in Memory of E. J. Hannan (eds P. M. ROBINSON and M. ROSENBLATT). New York: Springer-Verlag
    • TAQQU, M. S. and TEVEROVSKY, V. (1996) Semi-parametric graphical estimation techniques for long-memory data. In Athens Conference on Applied Probability and Time Series Analysis Vol. II: Time Series Analysis in Memory of E. J. Hannan. Vol. 115 of Lecture Notes in Statistics (eds P. M. ROBINSON and M. ROSENBLATT). New York: Springer-Verlag, pp. 420-32.
    • (1996) Lecture Notes in Statistics , vol.115 , pp. 420-432
    • Taqqu, M.S.1    Teverovsky, V.2
  • 34
    • 0002346987 scopus 로고    scopus 로고
    • On estimating the intensity of long-range dependence in finite and infinite variance series
    • (eds R. ADLER, R. FELDMAN and M. S. TAQQU). Boston: Birkhäuser
    • TAQQU, M. S. and TEVEROVSKY, V. (1998) On estimating the intensity of long-range dependence in finite and infinite variance series. In A Practical Guide to Heavy Tails: Statistical Techniques and Applications (eds R. ADLER, R. FELDMAN and M. S. TAQQU). Boston: Birkhäuser, pp. 177-217.
    • (1998) A Practical Guide to Heavy Tails: Statistical Techniques and Applications , pp. 177-217
    • Taqqu, M.S.1    Teverovsky, V.2
  • 35
    • 0030107894 scopus 로고    scopus 로고
    • Approximation power of biorthogonal wavelet expansions
    • UNSER, M. (1996) Approximation power of biorthogonal wavelet expansions. IEEE Transactions on Signal Processing 44(3), 519-27.
    • (1996) IEEE Transactions on Signal Processing , vol.44 , Issue.3 , pp. 519-527
    • Unser, M.1
  • 36
    • 0034274661 scopus 로고    scopus 로고
    • Meaningful MRA initialisation for discrete time series
    • VEITCH, D., TAQQU, M. S. and ABRY, P. (2000) Meaningful MRA initialisation for discrete time series. Signal Processing 80, 1971-83.
    • (2000) Signal Processing , vol.80 , pp. 1971-1983
    • Veitch, D.1    Taqqu, M.S.2    Abry, P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.