Interpolation and Prediction

  • John Lamperti
Part of the Applied Mathematical Sciences book series (AMS, volume 23)


In this chapter we will take a closer look at certain important questions about stationary sequences. In the case of interpolation, we assume that a stationary process (discrete time) is being recorded continuously, but that one or more observations are missed (perhaps while the experimenter is out to lunch). It is then desired to reconstruct the missing observations as well as possible using all the others, both earlier and later than the ones which were omitted. For prediction, on the other hand, we assume that the entire history of the process is known up to a certain point in time, and on the basis of these observations one or more of the future values must be estimated as accurately as possible. Still another problem, which we won’t discuss here, involves filtering an observed process which consists of a “desired signal” plus “noise” in order to recover the signal alone from the combination. Once again, Wiener’s Cybernetics is a source of interesting historical background.


Spectral Density Prediction Error Fourier Series Spectral Representation Spectral Decomposition 
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. M. Riesz (1916): “Über die Randwerte einer analytischen Funktion,” Skandinaviske Mathematikerkongres 4, pp. 27–44.Google Scholar

Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • John Lamperti
    • 1
  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA

Personalised recommendations