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Innovations and Wold decompositions of stable sequences
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  • Published: September 1988

Innovations and Wold decompositions of stable sequences

  • Stamatis Cambanis1,
  • Clyde D. Hardin Jr.1 nAff2 &
  • Aleksander Weron1 nAff3 

Probability Theory and Related Fields volume 79, pages 1–27 (1988)Cite this article

  • 128 Accesses

  • 39 Citations

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Summary

For symmetric stable sequences, notions of innovation and Wold decomposition are introduced, characterized, and their ramifications in prediction theory are discussed. As the usual covariance orthogonality is inapplicable, the non-symmetric James orthogonality is used. This leads to right and left innovations and Wold decompositions, which are related to regression prediction and least p th moment prediction, respectively. Independent innovations and Wold decompositions are also characterized; and several examples illustrating the various decompositions are presented.

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Author information

Author notes
  1. Clyde D. Hardin Jr.

    Present address: The Analytic Sciences Corporation, 55 Walkers Brook Drive, 01867, Reading, MA, USA

  2. Aleksander Weron

    Present address: the Institute of Mathematics, Technical University, 50-370, Wroclaw, Poland

Authors and Affiliations

  1. Center for Stochastic Processes, Department of Statistics, University of North Carolina, 27599-3260, Chapel Hill, NC, USA

    Stamatis Cambanis, Clyde D. Hardin Jr. & Aleksander Weron

Authors
  1. Stamatis Cambanis
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  2. Clyde D. Hardin Jr.
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  3. Aleksander Weron
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Additional information

Research supported by the Air Force Office of Scientific Research Contract F49620 82 C 0009

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Cite this article

Cambanis, S., Hardin, C.D. & Weron, A. Innovations and Wold decompositions of stable sequences. Probab. Th. Rel. Fields 79, 1–27 (1988). https://doi.org/10.1007/BF00319099

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  • Received: 09 August 1985

  • Revised: 07 April 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00319099

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Keywords

  • Covariance
  • Stochastic Process
  • Probability Theory
  • Statistical Theory
  • Prediction Theory
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