Power spectrum estimation through autoregressive model fitting

  • Hirotugu Akaike


Power Spectral Density Autoregressive Model Limit Distribution Multiple Time Series Mutual Independence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Akaike, “A method of statistical identification of discrete time parameter linear systems,Ann. Inst. Statist. Math., 21 (1969), 225–242.MathSciNetzbMATHGoogle Scholar
  2. [2]
    H. Akaike, “Fitting autoregressive models for prediction,”Ann. Inst. Statist. Math., 21 (1969), 243–247.MathSciNetzbMATHGoogle Scholar
  3. [3]
    T. W. Anderson and A. M. Walker, “On the asymptotic distribution of the autocor-relations of a sample from a linear stochastic process,”Ann. Math. Statist., 35 (1964), 1296–1303.MathSciNetzbMATHGoogle Scholar
  4. [4]
    R. B. Blackman and J. W. Tukey,The Measurement of Power Spectra, New York, Dover, 1959.zbMATHGoogle Scholar
  5. [5]
    P. H. Diananda, “Some probability limit theorems with statistical applications,”Proc. Cambridge Philos. Soc., 49 (1953), 239–246.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    U. Grenander and M. Rosenblatt,Statistical Analysis of Stationary Time Series, John Wiley, New York, 1957.zbMATHGoogle Scholar
  7. [7]
    R. H. Jones, D. H. Crowell and L. E. Kapuniai, “Change detection model for serially correlated multivariate data,” Unpublished manuscript, 1968.Google Scholar
  8. [8]
    H. B. Mann and A. Wald, “On the statistical treatment of linear stochastic difference equations,”Econometrica, 11 (1943), 173–220.CrossRefMathSciNetzbMATHGoogle Scholar
  9. [9]
    H. B. Mann and A. Wald, “On stochastic limit and order relationships,”Ann. Math. Statist., 14 (1943), 217–226.MathSciNetzbMATHGoogle Scholar
  10. [10]
    E. Parzen, “Statistical spectral analysis (single channel case) in 1968,” Stanford University Statistics Department Technical Report, 11 (1968).Google Scholar
  11. [11]
    E. Parzen, “Multiple time series modelling,” Stanford University Statistics Department Technical Report, 12 (1968), (A paper presented at the Second International Symposium on Multivariate Analysis, Dayton, Ohio on June 20, 1968).Google Scholar
  12. [12]
    P. Whittle, “On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix,”Biometrika, 50 (1963), 129–134.MathSciNetzbMATHGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics 1969

Authors and Affiliations

  • Hirotugu Akaike

There are no affiliations available

Personalised recommendations