Direct Quadratic Spectrum Estimation with Irregularly Spaced Data

Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 25)


The Direct Quadratic Spectrum Estimation (DQSE) method was defined in Marquardt and Acuff, 1982. Some of the theoretical properties of DQSE were explored. The method was illustrated with several numerical examples. The DQSE method is versatile in handling data that have irregular spacing or missing values; the method is computationally stable, is robust to isolated outlier observations in irregularly spaced data, is capable of fine frequency resolution, makes maximum use of all available data, and is easy to implement on a computer. Moreover, DQSE, coupled with irregularly spaced data, can provide a powerful diagnostic tool because irregularly spaced data are inherently resistant to aliasing problems that often are a limitation with equally spaced data.


Spectral Window Nyquist Frequency Outlier Data Point Irregular Spacing Poisson Sampling 
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  1. Box, G.E.P. and G. M. Jenkins (1970), “Time-Series Analysis, Forecasting and Control”, Holden-Day, San Francisco, CA, 2nd Ed. (1976).zbMATHGoogle Scholar
  2. Blackman, R. B. and J. W. Tukey (1959), “The Measurement of Power Spectra”, Dover Publications, New York.zbMATHGoogle Scholar
  3. Dunsmuir, W. (1981), “Estimation for Stationary Time Series when Data are Irregularly Spaced or Missing”, Applied Time Series Analysis II, Academic Press, New York and London, pp. 609–649.Google Scholar
  4. Findley, D. F., Ed. (1978), “Applied Time Series Analysis”, Academic Press, New York, 345 pp.zbMATHGoogle Scholar
  5. Gaster, M. and J. B. Roberts (1975), “Spectral Analysis of Randomly Sampled Signals”, J. Inst. Maths. Applics., 15, pp. 195–216.zbMATHCrossRefGoogle Scholar
  6. Gaster, M. and J. B. Roberts (1977), “The Spectral Analysis of Randomly Sampled Records by a Direct Transform”, Proc. Roy. Soc. London A, 354, pp. 27–58.MathSciNetCrossRefGoogle Scholar
  7. Haykin, S., Ed. (1979), “Nonlinear Methods of Spectral Analysis”, Springer-Verlag, Berlin, 247 pp.zbMATHGoogle Scholar
  8. Jones, R. H. (1962a), “Spectral Estimates and Their Distributions”, Skandinavisk Aktuarietidskrift, Part I and Part II, pp. 39-153.Google Scholar
  9. Jones, R. H. (1962b), “Spectral Analysis with Regularly Missed Observations”, Ann. Math. Statist., 33, pp. 455–461.MathSciNetzbMATHCrossRefGoogle Scholar
  10. Jones, R. H. (1970), “Spectrum Estimation with Unequally Spaced Observations”, Proc. Kyoto Int’l Conf. on Circuit and Syst. Theory, Instit. Electron. and Commun. Engrs. of Japan, pp. 253-254.Google Scholar
  11. Jones, R. H. (1971), “Aliasing with Unequally Spaced Observations”, J. Appl. Meteorol., 11, pp. 245–254.CrossRefGoogle Scholar
  12. Jones, R. H. (1972), “Spectrum Estimation with Missing Observations”, Ann. Instit. Statist. Math., 23, pp. 387–398.CrossRefGoogle Scholar
  13. Jones, R. H. (1975), “Estimation of Spatial Wavenumber Spectra and Falloff Rate with Unequally Spaced Observations”, J. Atmos. Sci., 32, pp. 260–268.CrossRefGoogle Scholar
  14. Jones, R. H. (1977), “Spectrum Estimation from Unequally Spaced Data”, Fifth Conference on Probability and Statistics, Amer. Meterol. Soc., Boston, Preprint Volume, pp. 277-282.Google Scholar
  15. Jones, R. H. (1979), “Fitting Rational Spectra with Unequally Spaced Data”, Sixth Conf. on Probability and Statistics in Atmospheric Sciences, Amer. Meteorol. Soc, Boston, Preprint Volume, pp. 231-234.Google Scholar
  16. Jones, R. H. (1980), “Maximum Likelihood Fitting of ARMA Models to Time Series with Missing Observations”, Technometrics, 22, pp. 389–395.MathSciNetzbMATHGoogle Scholar
  17. Jones, R. H. (1981), “Fitting a Continuous Time Autoregression to Discrete Data”, Applied Time Series Analysis II, Academic Press, New York and London, pp. 651–682.Google Scholar
  18. Marquardt, D. W. and S. K. Acuff (1982), “Direct Quadratic Spectrum Estimation from Unequally Spaced Data”, Applied Time Series Analysis, O. D. Anderson and M. R. Perryman (Editors), North Holland Publ. Co., Amsterdam.Google Scholar
  19. Masry, E. and M. C. Lui (1975), “A Consistent Estimate of the Spectrum by Random Sampling of the Time Series”, SIAM J. Appl. Math., 28, pp. 793–810.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Masry, E. and M. C. Lui (1976), “Discrete-Time Spectral Estimation of Continuous Parameter Processes — A New Consistent Estimate”, IEEE Trans. Information Theory, IT-22, pp. 298–312.MathSciNetCrossRefGoogle Scholar
  21. Masry, E. (1983), “Spectral and Probability Density Estimation from Irregularly Observed Data”, Symposium on Time Series Analysis of Irregularly Observed Data, College Station, TX, Springer-Verlag (this volume).Google Scholar
  22. Parzen, E. (1963), “On Spectral Analysis with Missing Observations and Amplitude Modulation”, Sankhya, Series A, 25, pp. 383–392.MathSciNetzbMATHGoogle Scholar
  23. Robinson, P. M. (1977), “Estimation of a Time Series Model from Unequally Spaced Data”, Stochastic Processes and Their Applications, 6, pp. 9–24.MathSciNetzbMATHCrossRefGoogle Scholar
  24. Shapiro, H. S. and R. A. Silverman (1960), “Alias-Free Sampling of Random Noise”, J. Soc. Indust. Appl. Math., 8, pp. 225–248.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Engineering DepartmentE. I. du Pont de Nemours and Company, Inc.WilmingtonUSA

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