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Structure of PC Sequences and the 3rd Prediction Problem

  • Andrzej MakagonEmail author
  • Abolghassem Miamee
Chapter
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

Founders of prediction theory formulated three prediction problems: extrapolation problem, interpolation problem, and the problem of positivity of the angle between the past and the future. The third one is strictly related to the question of representing the predictor as a series of past values of the process. All three have been solved in the case of stationary sequences, however, as far as we know in the case of periodically correlated sequences only the first prediction problem has been studied. The purpose of this chapter is to overview the third prediction problems.

Notes

Acknowledgments

This chapter deals with the theory of PC sequences, which is a very small part of a broad and multidisciplinary area of analysis of periodically correlated processes and cyclostationary signals. No paper on PCs would be complete without mentioning names as Hurd, Yavorskij, Leśkow, Dehay, Neapolitano, Weron, Wylomanska, who have shaped the theory and practice of periodically correlated processes (cf. Broszkiewicz-Suwaj et al. 2004; Cambanis et al. 1994; Dehay 1994; Dragan and Yavorskii 1985; Hurd 1974, 1989, 1991; Hurd and Leskow 1992a, b; Hurd et al. 2002; Hurd and Miamee 2007; Javors’kyj et al. 2003, 2007, 2010; Lenart et al. 2008; Leskow and Weron 1992; Neapolitano 2012; Weron and Wylomanska 2004; Wylomanska 2008) and provided a motivation for our study. We are grateful to Professor Leśkow for organizing annual workshops which give this diverse community an opportunity to share their research, experience, and ideas.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsHampton UniversityHamptonUSA

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