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Autoregressive and mixed autoregressive-moving average models and spectra

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Nonlinear Methods of Spectral Analysis

Part of the book series: Topics in Applied Physics ((TAP,volume 34))

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References

  1. A. van den Bos: IEEE Trans. IT-17, 493–494 (1971)

    Google Scholar 

  2. J. P. Burg: “Maximum entropy spectral analysis”, in 37th Ann. Intern. Meet. Soc. Explor. Geophys., Oklahoma City, Okla., Oct. (1967)

    Google Scholar 

  3. J.P.Burg: “A new analysis technique for time series data”. Adv. Study Inst. on Signal Processing NATO, Enschede, Holland (1968)

    Google Scholar 

  4. J.P.Burg: “Maximum entropy spectral analysis”; Ph.D. Thesis, Stanford University, Palo Alto, Calif. (1975)

    Google Scholar 

  5. H. Wold: A Study in the Analysis of Stationary Time Series (Almqvist and Wiksell, Uppsala 1938)

    MATH  Google Scholar 

  6. S. Treitel, P. R. Gutowski, E. A. Robinson: “Empirical spectral analysis revisited”, in Topics in Numerical Analysis, ed. by J.H. Miller (Academic Press, New York 1977) pp. 429–446

    Google Scholar 

  7. R. H. Jones: Technometrics 7, 531–542 (1965)

    MathSciNet  Google Scholar 

  8. R. B. Blackman, J. W. Tukey: The Measurement of Power Spectra from the Point of View of Communications Engineering (Dover, New York 1959)

    MATH  Google Scholar 

  9. L.J. Griffiths: IEEE Trans. ASSP-23, 207–222 (1975)

    Google Scholar 

  10. A.J.Jurkevics, T.J.Ulrych: “Representing and simulating strong ground motion”. B.S.S.A. 68 (3),781–801 (1978)

    Google Scholar 

  11. M.Ooe: Geophys. J. R. Astron. Soc. 53, 445–457 (1978)

    Article  ADS  Google Scholar 

  12. G.T.Wilson: SIAM J. Num. Anal. 6,1 (1969)

    Article  ADS  Google Scholar 

  13. E. A. Robinson: “Recursive decomposition of stochastic processes”, in Econometric Model Building, ed. by H.O. Wold (North-Holland, Amsterdam 1964) pp. 111–168

    Google Scholar 

  14. T.J. Ulrych, T. N. Bishop: Rev. Geophys. 13, 183–200 (1975)

    Article  ADS  Google Scholar 

  15. J.Makhoul: Proc. IEEE 63, 561–580 (1975)

    Article  ADS  Google Scholar 

  16. T.J.Ulrych, R.W.Clayton: Phys. Earth Planet. Inter. 12, 188–200 (1976)

    Article  ADS  Google Scholar 

  17. J. D. Markel, A. H. Gray: Linear Prediction of Speech, Communication and Cybernetics, Vol. 12 (Springer, Berlin, Heidelberg, New York 1976)

    Book  MATH  Google Scholar 

  18. J. Scargle: “Studies in Astronomical Time Series Analysis: Modeling Random Processes in the Time Domain”. NASA Tech. Memo. (1976)

    Google Scholar 

  19. G. E. P. Box, G. M. Jenkins: Time Series Analysis: Forecasting and Control, rev. ed. (Holden-Day 1976)

    Google Scholar 

  20. G. U. Yule: Philos. Trans. R. Soc. London, Ser. A 226, 267–298 (1927)

    Article  ADS  Google Scholar 

  21. D. E. Smylie, G. K. C. Clarke, T. J. Ulrych: Methods Comput. Phys. 13, 391–430 (1973)

    Google Scholar 

  22. J. A. Edward, M. M. Fitelson: IEEE Trans. IT-19, 232 (1973)

    Google Scholar 

  23. R. E. Kromer: “Asymptotic properties of the autoregressive spectral estimator”; Ph.D. dissertation, Tech. Rpt. 13, Dept. of Statistics, Stanford University, Stanford, Calif. (1969)

    Google Scholar 

  24. H.Akaike: Ann. Inst. Statist. Math. 21, 407–419 (1969)

    Article  MathSciNet  Google Scholar 

  25. K.N.Berk: Ann. Statistics 2, 489–502 (1974)

    Article  MathSciNet  Google Scholar 

  26. A. B. Baggeroer: IEEE Trans. IT-22, 534–545 (1976)

    MathSciNet  Google Scholar 

  27. H. Akaike: Ann. Inst. Statist. Math. 22, 203–217 (1970)

    Article  MathSciNet  Google Scholar 

  28. H. Akaike: “Use of an information theoretic quantity for statistical model indentification”, in Proc. 5th Hawaii Intern. Conf. on System Sciences, 99–101 (1972)

    Google Scholar 

  29. H. Akaike: IEEE Trans. AC-19, 716–723 (1974)

    MathSciNet  Google Scholar 

  30. T. E.Landers, R. T.Lacoss: IEEE Trans. GE-15 (1), 26–33 (1977)

    ADS  Google Scholar 

  31. E.Parzen: “Multiple time series: Determining the order of approximating autoregressive schemes”; Tech. Rpt. 23, Statistical Sci. Div., State Univ. New York at Buffalo (1976)

    MATH  Google Scholar 

  32. S. L. Marple: “Resolution of conventional Fourier, autoregressive, and special ARMA methods of spectrum analysis”. IEEE Intern. Conf. on ASSP, Hartford, Conn. (1977)

    Google Scholar 

  33. O. I. Frost: “Power spectrum estimation”, in 1976 NATO Advanced Study Institute on Signal Processing with Emphasis on Underwater Acoustics, Portovenere (La Spezia), Italy (1976)

    Google Scholar 

  34. G. M. Jenkins, D. G. Watts: Spectral Analysis and its Applications (Holden-Day, San Francisco 1969)

    MATH  Google Scholar 

  35. S. Treitel, T. J. Ulrych: IEEE Trans. ASSP-27, 99–100 (1979)

    Google Scholar 

  36. E. A. Robinson: “Structural properties of stationary stochastic processes with applications”, in Proc. of the Symposium on Time Series Analysis (Wiley and Sons, New York 1963) pp. 170–196

    Google Scholar 

  37. E. A. Robinson: Statistical Communication and Detection (Charles Griffin, London 1967) pp. 172–174

    Google Scholar 

  38. E. A.Guillemin: The Mathematics of Circuit Analysis (Wiley and Sons, New York 1949)

    MATH  Google Scholar 

  39. K. L. Peacock, S. Treitel: Geophys. 34, 155–169 (1969)

    Article  Google Scholar 

  40. N. Levinson: J. Math. Phys. 25, 261–278 (1947)

    Article  MathSciNet  Google Scholar 

  41. J. F. Claerbout: Fundamentals of Geophysical Data Processing (McGraw-Hill, New York 1976)

    Google Scholar 

  42. N.O. Andersen: Geophys. 39, 69–72 (1974)

    Article  Google Scholar 

  43. A. H. Nuttal: “Scientific and Engineering Studies: Spectral Estimation”; Naval Underwater Systems Center (1978)

    Google Scholar 

  44. R. L. Kayshap, A. R. Rao: Automatica 9, 175–183 (1973)

    Article  Google Scholar 

  45. R. L. Kayshap: IEEE Trans. AC-19,13–21 (1974)

    Google Scholar 

  46. A. J.Berkhout, P.R. Zaanen: Geophys. Prospect. XXIV (1), 141–197 (1976)

    Article  ADS  Google Scholar 

  47. W. Y. Chen, G. R. Stegen: J. Geophys. Res. 79, 3019–3022 (1974)

    Article  ADS  Google Scholar 

  48. D. N. Swingler: “Fundamental limitations of Burg's maximum entropy spectral analysis technique” (unpublished manuscript 1977)

    Google Scholar 

  49. J.Makhoul: IEEE Trans. ASSP 25, 423–428 (1977)

    Article  Google Scholar 

  50. E. Widrow, M. E. Hoff: “Adaptive switching circuits”, in IRE WESCON Convention Rec., Pt. 4, pp. 96–104 (1960)

    Google Scholar 

  51. L.J.Griffiths, R.Prieto-Diaz: IEEE Trans. GE-15 (1), 13–25 (1977)

    Google Scholar 

  52. H. Robbins, S. Monroe: Ann. Math. Stat. 22, 400–407 (1951)

    Article  Google Scholar 

  53. B. Widrow: “Adaptive filters”, in Aspects of Network and System Theory, ed. by R. E. Kalman, N. DeClaris (Holt, Rinehart, and Winston, New York 1970)

    Google Scholar 

  54. R.J.Wang, S.Treitel: Geophys. Prospect. XIX (4) 718–728 (1971)

    Article  ADS  Google Scholar 

  55. B.Widrow, J.M. McCool, M.G. Larimore, C.R.Johnson, Jr.: Proc. IEEE 64,1521–1529 (1976)

    Article  MathSciNet  Google Scholar 

  56. E. A. Robinson, S.Treitel: Geophys. Prospect. 25, 434–459 (1977)

    Article  ADS  Google Scholar 

  57. M.S.Bartlett: J. R. Statist. Soc. Suppl. B8, 27–41 (1946)

    Article  MathSciNet  Google Scholar 

  58. J. Perl, L. L. Scharf: IEEE Trans. ASSP-25 (2), 143–151 (1977)

    Google Scholar 

  59. M.Pagano: Ann. Statistics 2, 99–108 (1974)

    Article  MathSciNet  Google Scholar 

  60. R.K.Mehra: IEEE Trans. AC-16, 12–21 (1971)

    MathSciNet  Google Scholar 

  61. D. J. Krause, D. Graupe: “identification of autoregressive moving-average predictor models”, in Proc. 2nd Symp. on Nonlinear Estimation Theory and Its Applications, Harold W. Sorenson, chairman, 174–182 (1971)

    Google Scholar 

  62. W. Gersch: IEEE Trans. AC-15, 583–588 (1970)

    MathSciNet  Google Scholar 

  63. H. Akaike: Biometrika 60, 2, 255–265 (1973)

    Article  MathSciNet  Google Scholar 

  64. H. Akaike, E. Arahata, T.Ozaki: TIMSAC-74, A time series analysis and control program package (1). Computer Science Monographs, No. 5, A publication of the Inst. Statist. Math. (1975)

    Google Scholar 

  65. W.Gersch, N.N.Nielson, H. Akaike: J. Sound Vib. 31 (3), 295–308 (1973)

    Article  ADS  Google Scholar 

  66. H. Akaike: Ann. Inst. Statist. Math. 26, 363–387 (1974)

    Article  MathSciNet  Google Scholar 

  67. H.Tong: IEEE Trans. IT-21, 476–480 (1975)

    Google Scholar 

  68. H.Tong: IEEE Trans. IT-22, 493–496 (1976)

    Google Scholar 

  69. H.Tong: IEEE Trans. IT-23, 409–410 (1977)

    Google Scholar 

  70. V.F.Pisarenko: Geophys. J. R. Astron. Soc. 33, 347–366 (1973)

    Article  ADS  Google Scholar 

  71. W. Gersch, D. R. Sharpe: IEEE Trans. AC-18, 367–369 (1973)

    Google Scholar 

  72. E. H. Satorius, S. T. Alexander: “High resolution spectral analysis of sinusoids in correlated noise”, in IEEE Intern. Conf. on Acoust., Speech, and Signal Processing, Tulsa, Okla. (1978)

    Google Scholar 

  73. W. C. Devidon: Comput. J. 10, 406–410 (1968)

    Article  MathSciNet  Google Scholar 

  74. W. C. Devidon: “Variance algorithms for minimization”, in Optimization, ed. by R. Fletcher (Academic Press, London 1969) pp. 13–20

    Google Scholar 

  75. H. Akaike: “Information theory and extension of the maximum likelihood principle”, in Proc. 2nd Intern. Symp. on Information Theory, ed. by B.N.Petrov, F.Csaki (Akademiai Kiado, Budapest 1973) pp. 267–281

    Google Scholar 

  76. S. Kullback, R. A. Leibler: Ann. Math. Statistics 22, 79–86 (1951)

    Article  MathSciNet  Google Scholar 

  77. H.Jeffreys: Mon. Not. Roy. Astron. Soc. 100, 139–155 (1940)

    Article  ADS  Google Scholar 

  78. G. Colombo, I. I. Shapiro: Nature 217, 156–157 (1968)

    Article  ADS  Google Scholar 

  79. R.O. Vincente, S. Yumi: Publ. Int. Latit. Obs. Mizusawa 7, 1, 41–50 (1969)

    ADS  Google Scholar 

  80. R.O. Vincente, S. Yumi: Publ. Int. Latit. Obs. Mizusawa 7, 2, 109–112 (1970)

    ADS  Google Scholar 

  81. S. Yumi: 1971–1976, Ann. Rpt. of IPMS for the years 1969–1974

    Google Scholar 

  82. M.Ooe, Y. Kaneko, H. Akaike: Publ. Int. Latit. Obs. Mizusawa 11, 1, 1–9 (1977)

    ADS  Google Scholar 

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Authors
  1. T. J. Ulrych
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  2. M. Ooe
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Simon Haykin Ph, D., D. Sc.

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Ulrych, T.J., Ooe, M. (1979). Autoregressive and mixed autoregressive-moving average models and spectra. In: Haykin, S. (eds) Nonlinear Methods of Spectral Analysis. Topics in Applied Physics, vol 34. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12386-5_10

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  • DOI: https://doi.org/10.1007/3-540-12386-5_10

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