Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-30T21:23:35.515Z Has data issue: false hasContentIssue false
  • English
  • Français

Spectral inference over narrow bands

Published online by Cambridge University Press:  14 July 2016

E. J. Hannan  and
P. J. Thomson
E. J. Hannan
Affiliation:
Australian National University
P. J. Thomson
Affiliation:
Australian National University
Get access Rights & Permissions [Opens in a new window]

Extract

We consider a vector, discrete, time sequence x(n), n = 0, ± 1 ···, of p components Xj(n), j = 1, ··· p. For the most part we shall assume x(n) to be strictly stationary and with finite variances. Thus if μ is the mean vector we shall have

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 1 , March 1971 , pp. 157 - 169
Copyright
Copyright © Applied Probability Trust 1971 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brillinger, D. R. (1969) Asymptotic properties of spectral estimates of second order. Biometrika 56, 375–390.Google Scholar
Cooley, J. W. and Tukey, J. W. (1965) An algorithm for the machine calculation of complex Fourier series. Math. Comp. 19, 297–301.Google Scholar
Gnedenko, B. V. and Kolmogoroff, A. N. (1954) Limit Distributions for Sums of Independent Random Variables. Addison-Wesley, Reading, Mass.Google Scholar
Jones, R. H. (1969) Phase free estimation of coherence. Ann. Math. Statist. 40, 540–548.Google Scholar
Munk, W. H. and Cartwright, D. E. (1966) Tidal spectroscopy and prediction. Phil. Trans. 259, 533–581.Google Scholar
Rosenblatt, M. (1956) A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. U.S.A. 42, 43–47.Google Scholar
Rozanov, Yu. A. (1967) Stationary Random Processes. Holden-Day, San Francisco.Google Scholar