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Original Articles

Effects of the presence of a harmonic term on the spectral factorisation procedureFootnote1

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Pages 317-349 | Published online: 27 Jun 2007

References

  • Abramowitz , M. and Begun , I.A. 1965 . Handbook of Mathematical Functions , New York : Dover .
  • Akaike , H. 1970 . Statistical predictor identification . Ann. Inst, Statist Math , 22 : 203 – 217 .
  • Akakie , H. Information theory and an extension of the maximum likelihood principle . 2nd International Symposium on Information Theory . Edited by: Petbov , B.N. and Csaki , F. pp. 267 – 281 . Budapest : Akademia Kiado .
  • Bennet , B.M. 1955 . Note on the moments of the logarithmic non-central %2 and z distributions . Ann. Inst. Statist. Math , 7 : 57 – 61 .
  • Berk , K.N. 1974 . Consistent autoregressive spectral estimates . Ann. Statist , 2 : 489 – 502 .
  • Bhansali , R.J. 1973 . A simulation study of the Wiener-Kolmogorov predictor . Sankhya , 35 : 357 – 376 .
  • Bhansali , R.J. 1974 . Asymptotic properties of the Wiener-Kolmogorov predictor. I . J. Roy. Statist. Soc , 36 : 61 – 73 .
  • Bhansali , R.J. 1976 . Estimation of the moving average representation of a stationary nondeterministic process . Biometrika , 63 : 408 – 410 .
  • Bhansali , R.J. 1977a . Asymptotic properties of the Wiener-Kolmogorov predictor. II . J. Roy. Statist. Soc , 39 : 66 – 72 .
  • Bhansali , R.J. 1977b . “ An application of Priestley's P(λ) test to the-Southend tide heights data ” . In Recent Developments in Statistics , 351 – 356 . Amsterdam : North Holland .
  • Bhansali , R.J. 1978 . Linear prediction by autoregressive model fitting in the time domain . Ann. Statist , 6 : 224 – 231 .
  • Bhansali , R.J. 1979 . A mixed spectrum analysis of the Lynx data . J. Roy. Statist. Soc A , 142 : 199 – 209 .
  • Bhansali , R.J. and Downham , D.Y. 1977 . Some properties of the order of an autoregressive model selected by a generalisation of Akaike's FPE criterion . Biometrika , 64 : 547 – 551 .
  • Bloomfield , P. 1973 . An exponential model for the spectrum of a scalar time series . Biometrika , 60 : 217 – 226 .
  • Box , G.E.P. and Jenkins , G.M. 1970 . Time Series Analysis: Forecasting and Control , San Francisco : Holden Day .
  • Brillinger , D.R. 1975 . Time Series: Data Analysis and Theory , New York : Holt, Rinehart and Winston .
  • Cameron , M.A. 1978 . The prediction variance and related statistics for stationary time series . Biometrika , 65 : 283 – 296 .
  • Campbell , M.J. and Walker , A.M. 1977 . A survey of statistical work on the McKenzie River series of annual Canadian Lynx trappings for the years 1921-1934 and a new analysis . J. Roy. Statist. Soc , 140 : 411 – 431 .
  • Davis , H.T. and Jones , R.H. 1968 . Estimation of the innovation variance of a stationary time series . J. Amer. Statist. Assoc , 63 : 141 – 149 .
  • Doob , J.L. 1953 . Stochastic Processes , New York : Wiley .
  • Gentleman , W.M. and Sande , G. Fast Fourier transforms for fun and profit . 1966 Fall Joint Computer Conference . Spartan, Washington. Vol. 28 , pp. 563 – 578 . AFIPS
  • Granander , U. and Rosenblatt , M. 1957 . Statistical Analysis of Stationary Time Series , New York : Wiley .
  • Hannan , E.J. 1961 . Testing for a jump in the spectral function . J. Roy. Statist. Soc B , 23 : 394 – 404 .
  • Hannan , E.J. and Nicholls , D.F. 1977 . The estimation of the prediction error variance . J. Amer. Statist. Assoc , 72 : 834 – 840 .
  • Huzii , M. 1980 . “ On an autoregressive model fitting and discrete spectra ” . In Recent Developments in Statistical Inference and Data Analysis , Edited by: Matusita , K. 131 – 135 . Amsterdam : North Holland .
  • Jenkins , G.M. and Watts , D.G. 1968 . Spectral Analysis and its Applications , San Francisco : Holden Day .
  • Johnson , N.L. 1949 . Systems of frequency curves generated by methods of translation . Biometrika , 36 : 149 – 176 .
  • Jones , R.H. 1976 . Estimation of the innovation generalised variance of a niultivariate stationary time series . J, Amer. Statist. Assoc , 71 : 386 – 388 .
  • Kendall , M.G. and Stuart , A. 1973 . The Advanced Theory of Statistics , Vol. II , London : Griffin .
  • McClave , J.T. 1975 . Subset autoregression . Technometrics , 17 : 213 – 220 .
  • MacNeill , I. 1974 . Tests for periodic components in multiple time series . Biometrika , 61 : 57 – 70 .
  • Parzen , E. 1974 . Some recent advances in time series modelling . IEEE Trans. Auto. Control , AC-19 : 723 – 730 .
  • Patnaik , P.B. 1949 . The non-central χ2 and F-distribution and their applications . Biometrika , 36 : 203 – 232 .
  • Priestley , M.B. 1962a . The analysis of stationary processes with mixed spectrum - I . J. Roy. Statist. Assoc. B , 24 : 215 – 233 .
  • Priestley , M.B. 1962a . The analysis of stationary processes with mixed spectrum - II . J. Roy. Statist. Assoc , 24 : 511 – 529 .
  • Rao , C.R. 1973 . Linear Statistical Inference and its Applications , New York : Wiley .
  • Shibata , R. 1977 . Convergence of least squares estimates of autoregressive parameters . Austral. J. Statist , 19 : 226 – 235 .
  • Titchmarsh , E. 1932 . The Theory of Functions , Oxford : Clarendon .
  • Tong , H. 1977 . Some comments on the Canadian Lynx data . J. Roy. Statist. Assoc A , 140 : 432 – 436 .
  • Whittle , P. 1954 . The statistical analysis of a seiche record . J. Marine Research , 13 : 76 – 100 .
  • Weiner , N. 1949 . Extrapolation, Interpolation and Smoothing of Stationary Time Series , New York : Wiley .
  • Woodroofe , M.B. and Van Ness , J.W. 1967 . The maximum deviation of sample spectral densïties . Ann. Math. Statist , 38 : 1558 – 1569 .

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