On smoothing techniques for the removal of periodic noise of known period

  • R. S. Anderssen
  • E. Seneta
Article

Abstract

This paper is concerned with the analysis of the linear modely(n)=Xβ(n)+S(n)+γ(n) for the data sequencey(n) (n=1, 2, ..., N) whereX={xIJ} is a knownJ × M matrix of full rankM. Here, theβ(n) are unknown vectors, which we wish to estimate for eachn; S(n) (n=1, 2, ..., N) is a periodic component (which we wish to estimate or remove) superimposed on the linear structureXβ(n); andγ(n) is an error vector which is specified as having zero expectation (with possible further properties). Such models commonly occur in geophysical data analysis.

Key words

data processing Fourier analysis moving average time series 

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Copyright information

© Plenum Publishing Corporation 1971

Authors and Affiliations

  • R. S. Anderssen
    • 1
  • E. Seneta
    • 2
  1. 1.Computer CentreThe Australian National UniversityAustralia
  2. 2.Statistics DepartmentThe Australian National UniversityAustralia

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