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Structure of Periodically Distributed Stochastic Sequences

In: Stochastic Processes

Author

Listed:
  • Andrzej Makagon

    (Michigan State University, Dept. of Statistics and Probability
    Technical University of Wroclaw, Institute of Mathematics)

  • Habib Salehi

    (Michigan State University, Dept. of Statistics and Probability)

Abstract

It is shown that every periodically distributed (PD) stochastic sequence with a period T can be represented as a linear combination of the coordinates of an associated T-variate strictly stationary sequence. This result extends a theorem of Gladyshey for periodically correlated sequences to stochastic sequences with possibly infinite second moment. It is proved that if a PD sequence, is SαS then the associated strictly stationary sequence is also SαS, and that it shares the regularity properties of the underlying PD sequence. As a byproduct new prools of most of Gladyshev’s results in [2] are obtained.

Suggested Citation

  • Andrzej Makagon & Habib Salehi, 1993. "Structure of Periodically Distributed Stochastic Sequences," Springer Books, in: Stamatis Cambanis & Jayanta K. Ghosh & Rajeeva L. Karandikar & Pranab K. Sen (ed.), Stochastic Processes, pages 245-251, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-7909-0_27
    DOI: 10.1007/978-1-4615-7909-0_27
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